Operation Libero und die Forschungsgruppe Databases and Information Systems (DBIS) laden ein, euch als Team von drei oder vier Personen in der Kunst der Prompt Battles zu üben oder als Zuschauer*in zu voten. Die Teams werden vor Ort gegründet, Vorkenntnisse brauchst du nicht.

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Und hier noch eine kleine Ankündigung: Bereits jetzt ist bekannt, dass Nationalrätin **Sibel Arslan** und **Franziska Stier**, Geschäftsführung BastA!, sich mit euch im Prompten messen werden! Wir freuen uns sehr darüber und sind dabei, den Kreis von weiteren spannenden, lokal engagierten Mitspieler*innen zu erweitern.

**Bekannt oder nicht, am Ende zählt der Applaus des Publikums.** Den Gewinner*innen winken neben Ruhm und Anerkennung unser schönes Europa-Täschli mit vielen spannenden und trinkbaren Überraschungen!

**Wie anmelden?**

**Mitmach-Ticket**: Du willst mitprompten? Hol dir ein Mitmach-Ticket.**Publikumsticket**: Um dabei zu sein und zu voten, ist das Publikumsticket genau das Richtige für dich!

**Wie sieht der Ablauf aus? **

- Ab 19 Uhr: Warm-up mit den Entwickler*innen der "Prompt-o-Lympics"
- Punkt 20 Uhr: Start
- Bis 22 Uhr: Einladung zum Apéro

Using weights for fun and profit: Weighted sparse and low-rank approximation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>No Transparency for Smart Toys

Tags: TAG Events DMI]]>

Inequalities for Schwarz maps on matrix algebras

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

This talk will present joint work with Mueller-Hermes and Zhang in which duality is exploited to give simple proofs of known and new inequalities for Schwarz maps. It will be shown how these yield celebrated convexity and concavity theorems, such as those of Lieb and Epstein as simple corollaries. The ideas may be applied in a more elaborate operator algebra setting, but by presenting them in the matrix algebra setting, the talk will require no specialized knowledge as background.

]]>Spectral analysis of polaron models in the strong coupling limit

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Ground state (in-)stability and long-time behavior in multi-dimensional Schrödinger equations]]>

Cusp formation of singular vortex patches

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Rigidity of critical points of degenerate polyconvex energies

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Nash's isometric embedding

Tags: TAG Events DMI]]>

The Swiss Comic Con

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Am Stand des Departements werden Exponate der Databases and Information Systems (DBIS) Forschungsgruppe, der Privacy-Enhancing Technologies (PET) Forschungsgruppe und der High Performance Computing (HPC) Forschungsgruppe gezeigt.

Sie finden den Stand in Halle 1.1 mit der Standnummer 138.

]]>The third law of black hole thermodynamics and the black hole formation threshold

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

An introduction to Unlikely Intersections

Tags: TAG Events DMI]]>

CANCELLED

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Die Schweizerische Mathematische Gesellschaft lädt Doktorand*innen der Mathematik von Schweizer Universitäten sowie Postdocs zu einer eintägigen Veranstaltung ein, die eine Plattform für Präsentationen, Diskussionen und Erfahrungsaustausch bietet.

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

]]>

Identification of microstructural information from macroscopic boundary measurements in linear elasticity

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

This is joint work with T. Lochner (University of Augsburg).

For further information about the seminar, please visit this webpage.

]]>Zero-dispersion limit for the Benjamin-Ono Equation]]>

be-digital Forum 2024

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Weitere Informationen erhlaten Sie **hier**.

Self-similar solutions for the forced 3D Navier–Stokes Equations

Tags: TAG Events DMI]]>

Multiscale wave propagation in time-varying media

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Based on joint work with Bernhard Maier, we present a numerical multiscale method for spatially multiscale, (slowly) time-evolving coefficients. The method is inspired by the Localized Orthogonal Decomposition (LOD) and entails time-dependent multiscale spaces. We provide a rigorous a priori error analysis for the considered setting. Numerical examples illustrate the theoretical findings and investigate an adaptive approach for the computation of the time-dependent basis functions.

On the other hand, we will also briefly discuss the setting of spatially homogeneous, temporal multiscale coefficients. (Higher-order) multiscale expansions may help to interpret effective physical material properties and are numerically illustrated.

For further information about the seminar, please visit this webpage.

]]>Sharp nonuniqueness of the transport equation with Sobolev vector fields

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Automorphic forms in Number Theory

Tags: TAG Events DMI]]>

11.04.2024 16:15, Spiegelgasse 5, Raum 05.002

Global relaxation for kinetic alignment models and the problem of emergence arising in systems of collective behavior

Tags: TAG Events Perlenkolloquium, TAG Events DMI, TAG Events Forschung Mathematik]]>

11.04.2024 09:30 - 11.04.2024 16:10, Kollegienhaus, Hörsaal 120

Fifth Meeting

Tags: TAG Events DMI, TAG Events Zahlentheorie, TAG Events Forschung Mathematik]]>

Conference

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Forschung Informatik]]>

DS4S offers a unique opportunity to bring together research actors and stakeholders from cantonal universities, universities of applied sciences, federal institutes, federal agencies, and corporate R&D around contemporary questions and challenges pertaining to data-driven scientific discovery.

DS4S will feature presented contributions on topics encompassing AI for Medicine, Physics-Guided Machine Learning for Climate Modelling, AI & Robotics, Privacy safeguarding, Causality and Neuroscience. Open Research Data will also be put to the fore via a dedicated session. Among the distinguished speakers, Giusi Moffa, head of the Statistical Science Research Group at the Department of Mathematics and Computer Science, will be sharing her insights and expertise.

More information can be found **here**.

Volumetric approach to intermittency in fully developed turbulence

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Periods and o-minimality

Tags: TAG Events DMI]]>

Newton-Nash iterations in PDE

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Dynamics of mean-field Fermi systems with nonzero pairing]]>

In einer «Gameshow» treten menschliche Komponist*innen gegen AI-Kompositionen an.

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

In einer «Gameshow» tritt in fünf Kapiteln jeweils ein menschlicher Komponist gegen eine AI-Komposition an. Das Publikum hört pro Kapitel und Stück zwei Versionen und wählt, welches Stück AI, welches Mensch war. Die Stücke sind im Stil von Bach, Chopin, Messiaen, Bartok, Brahms komponiert und werden von einem menschlichen Ensemble gespielt (auch das Ensemble weiss nicht, was Mensch, was AI ist).

In Zusammenarbeit mit den Kompositionsklassen der Hochschule für Musik Basel komponieren herausragende Studierende den «menschlichen» Teil; der bekannte lettische Komponist Platons Buravickis «erstellt» die AI-Kompositionen. Faszinierende Visual Arts von Luca Scarzella und Michele Innocente begleiten die Vorstellung.

Die Aufführung wird moderiert und in Kollaboration mit dem Forschungsnetzwerk Responsible Digital Society RDS an der Universität Basel durch wissenschaftliche Intermezzi ergänzt. Beim anschliessenden Apéro mischen sich Wissenschaftler:innen vom AI-Ethiker bis zur AI-Medizinforscherin unter das Publikum und freuen sich auf Fragen zur künstlichen Intelligenz.

Die Veranstaltung wird mit einer Ansprache von Regierungsrat Conradin Cramer eröffnet. Bitte scannen Sie am Eingang der Voltahalle den QR-Code, um per Smartphone an den Abstimmungen teilnehmen zu können.

Early Bird-Tickets «Artificial Art – Human Composers vs. AI» (inkl. Apéro): 30 CHF Normalpreis 20 CHF reduziert (unter 28 Jahren). Freie Platzwahl.

]]>Model hierarchies in semiclassical semi-relativistic quantum physics: From Dirac-Maxwell to Euler-Poisson]]>

semiclassical semi-relativistic quantum dynamics. It is at the

center of a hierarchy of models from the Dirac-Maxwell equation to

the Euler-Poisson equation that are linked by asymptotic analysis of

small parameters such as Planck constant or inverse speed of light.

We discuss the models and their application in plasma and

accelerator physics as well as the many mathematical problems they

pose.

]]>Wave interaction with subwavelength resonators

Tags: TAG Events DMI]]>

14.03.2024 16:15, Spiegelgasse 5, Raum 05.002

Tumbling Downhill along a Given Curve

Tags: TAG Events Perlenkolloquium, TAG Events DMI]]>

wiggle along a circle on that plane and then will stop rolling.

We ask the inverse question: For which curves drawn on the inclined plane

$\real^2$ can one chisel a shape that will roll downhill following precisely

this prescribed curve and its translationally repeated copies?

This is a nice, and easy to understand problem, but the solution is quite

interesting.

(Based on work mostly with Y. Sobolev and T. Tlusty. After a Nature paper,

Solid-body trajectoids shaped to roll along desired pathways, August 2023.) ]]>

Riemann’s Uniformization Theorem

Tags: TAG Events DMI]]>

Landau damping near the Poisson equilibrium in R^3

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Roots of Unity Solving Polynomial Equations: Manin-Mumford

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Öffentliche Veranstaltung mit anschliessendem Apéro

Tags: TAG Events DMI]]>

**Reunion 2024: Vorträge und Apéro**

Prof. Dr. Mario Wüthrich von der ETH Zürich wird einen Vortrag halten zu *Discrimination and Fairness in Insurance Pricing* und im Anschluss präsentiert der Masterstudent Mathieu Jenni seine Abschlussarbeit. Nach den Referaten sind alle herzlich eingeladen zu einen Apéro.

Für die Vorträge und den Apéro ist keine Anmeldung erforderlich. Der Besuch der Veranstaltung ist von der SAV als Weiterbildung anerkannt (1 SAV-CP).

**Anmeldung AlumniEssen **

Das anschliessende AlumniEssen im *Ristorante Fiorentina* ist für Mitglieder von AlumniActuarialScience und solche, die es gerne werden wollen. Bitte anmelden **bis am 29. Januar 2024**: info@AlumniActuarialScience.ch.

Jubiläumsfeier

Tags: TAG Events Forschung Informatik, TAG Events DMI]]>

**Programm:**

Begrüssung Prof. Jiří Černý, Vorsteher Departement Mathematik und Informatik

Grusswort der Rektorin Prof. Dr. Dr. h.c. mult. Andrea Schenker-Wicki

**Teil 1: Zukunft der Informatik-Forschung**

- Vortrag Prof. Dr. Joachim Buhmann, ETH Zürich, Institut für Maschinelles Lernen

- Vortrag Dr. Yannic Kilcher, Gründer und CTO Deep Judge, Gründer Open Assistant, Youtuber

**Teil 2: Zukunft der Informatik-Lehre**

Podiumsdiskussion mit

- Prof. Dr. Joachim Buhmann, ETH Zürich, Institut für Maschinelles Lernen

- Brigitte Jäggi, Rektorin Gymnasium Muttenz

- Dr. Yannic Kilcher, Gründer und CTO Deep Judge, Gründer Open Assistant, Youtuber

- Dr. Gabriele Röger, Dozentin am Dep. Mathematik und Informatik, Universität Basel

- Deborah Strub, Leiterin Digitalinitiative be-digital der Handelskammer beider Basel

Moderation: Prof. Dr. Nadja Braun Binder, Vizerektorin People & Culture, Universität Basel

Im Anschluss sind Sie herzlich zu einem Apéro eingeladen.

]]>Was ist generative künstliche Intelligenz?

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Weitere Informationen erhlaten Sie **hier**.

Cubic Regularized Subspace Newton for Non-convex Optimization

Tags: TAG Events DMI]]>

Effective dynamics of high density Fermi gases

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Free boundary problems for the partially reflected Brownian motion: dimension of the Robin harmonic measure

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Stochastic approximation for shape optimization under uncertainty

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Joint work with: Kathrin Welker, Estefania Loayza-Romero, Tim Suchan

For further information about the seminar, please visit this webpage.

]]>Permanent features of 2d fluids

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

**Notice the special time!**

A posteriori error estimates robust with respect to nonlinearities and final time

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

A. Ern, I. Smears, M. Vohralík, Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems, *SIAM J. Numer. Anal.***55** (2017), 2811–2834.

A. Harnist, K. Mitra, A. Rappaport, M. Vohralík, Robust energy a posteriori estimates for nonlinear elliptic problems, HAL Preprint 04033438, 2023.

K. Mitra, M. Vohralík, A posteriori error estimates for the Richards equation, *Math. Comp.* (2024), accepted for publication.

K. Mitra, M. Vohralík, Guaranteed, locally efficient, and robust a posteriori estimates for nonlinear elliptic problems in iteration-dependent norms. An orthogonal decomposition result based on iterative linearization, HAL Preprint 04156711, 2023.

For further information about the seminar, please visit this webpage.

]]>Steady vortex rings with surface tension

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Boltzmann equation, hard sphere systems and their small and large deviations]]>

Boltzmann equation, hard sphere systems and their small and large deviations]]>

23.11.2023 16:15, Spiegelgasse 5, Raum 05.002

A big telescope and a big computer: how HPC and AI will enable next breakthroughs in our understanding of the Universe

Tags: TAG Events Forschung Informatik, TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

More information here.

Abstract:

The upcoming mega-telescopes, such as European Space Agency’s recently launched Euclid satellite, and the upcoming radio Square Kilometer Array (SKA), will provide images of our universe over 10 billion years of cosmic history, and enable us to study its evolution with unprecedented level of detail. In the framework of simulations-based inference, the big telescopes deliver a throve of high-resolution observations and big computers provide the feature-rich numerical theory prediction. By using AI trained on simulations and performing inference on observations, we will be able us to differentiate between complex models of dark matter, dark energy, modified gravity, and astrophysics; a task unattainable by classical pen-and-paper analysis. This way, big computers paired with big telescopes will enable next breakthroughs in our understanding of the universe. In this talk, I will review the current and future applications of HPC and AI in cosmology in astrophysics, focusing on areas where they already play an indispensable role. I will also present a number of yet-unsolved problems in data science, the solutions to which are critical for enabling next generation measurements in cosmology.

Microscopic derivation of a nonlinear Schrödinger equation with a nonlinear point interaction in 1D]]>

We assume introducing a tiny impurity located at the origin and considering that the interaction between every pair of bosons is mediated by the impurity through a three-body interaction. Moreover, by assuming short-range scaling and choosing an initial fully condensed state, we prove convergence of one-particle density operators in the trace-class topology. This is the first derivation of the so-called nonlinear delta model. This research is a collaborative work with Prof. Riccardo Adami. ]]>

Smooth Irreducible Curves in the Projective Space of Small Degree and Genus

Tags: TAG Events DMI]]>

Lerne das vielfältige Studienangebot der Universität Basel kennen, tausche dich mit Studierenden und Dozierenden aus und schnuppere Uni-Luft. Lasse dich von den Studiengangskoordinatorinnen bei Fragen zur Anmeldung, Vorkenntnissen und weiteren Themen beraten.

Tags: TAG Events DMI]]>

Linear Inviscid Damping in the 2D Euler-Boussinesq system in the periodic channel

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Energy conservation for fluid flows in an Onsager critical class

Tags: TAG Events DMI]]>

10.11.2023 14:00 - 11.11.2023 11:30, Philipp Habegger (Unibas), Özlem Imamoglu (ETHZ), Philippe Michel (EPFL), Maryna Viazovska (EPFL) , HS -101, Alte Universität, Rheinsprung 9, Universität Basel

Speakers: Anna Cadoret (Sorbonne Université), Pierre Colmez (CNRS, Sorbonne Université), Vesselin Dimitrov (Georgia Institute of Technology), Javier Fresán (Sorbonne Université), Kaisa Matomäki (University of Turku)

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Die Registrierung ist kostenlos, aber obligatorisch. Registrieren Sie sich bitte hier: Registrierung.

]]>A posteriori error estimates and adaptive error control for electromagnetic coefficient inverse problem in conductive media

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

All reconstruction algorithms are based on optimization approach for finding of stationary point of the Lagrangian. Derivation of a posteriori error estimates for the regularized solution and Tikhonov functional will be presented. Based on these estimates adaptive reconstruction algorithms are developed. Computational tests will show robustness of proposed algorithms in 3D.

For further information about the seminar, please visit this webpage.

]]>Deep Learning Talk by Spencer Frei (UC Davis)]]>

Spencer Frei is an Assistant Professor of Statistics at UC Davis. He is broadly interested in machine learning, statistics, and optimization, with a particular interest in understanding and improving deep learning. Prior to joining UC Davis, he was a postdoctoral fellow at the Simons Institute for the Theory of Computing at UC Berkeley, mentored by Peter Bartlett and Bin Yu as a part of the NSF/Simons Collaboration on the Theoretical Foundations of Deep Learning. He completed his PhD in Statistics at UCLA under the supervision of Quanquan Gu and Ying Nian Wu.

]]>A mean field planning approach to regularizations of the optimal transport problem

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Assuming the initial and terminal measures to have densities, we prove that the optimal curve remains positive and locally bounded in time. We focus on the case that the transport problem is set on a compact Riemannian manifold with Ricci curvature bounded below.

The approach follows ideas introduced by P.L. Lions in the theory of mean-field games about optimization problems with penalizing congestion terms. Crucial steps of our strategy include displacement convexity properties in the Eulerian approach and the analysis of distributional subsolutions to Hamilton-Jacobi equations.

The result provides a smooth approximation of Wasserstein-2 geodesics.

]]>The optimal transport problem: equivalent formulations and regularizations

Tags: TAG Events DMI]]>

06.11.2023 18:00 - 06.11.2023 20:00, Französische Botschaft in der Schweiz; Universität Basel, Universität Basel, Biozentrum, Hörsaal U1.131, Spitalstrasse 41, 4056 Basel

Vorträge und Podiumsdiskussion im Rahmen des Programms «La Nuit des idées»

Tags: TAG Events DMI]]>

Die Veranstaltung ist zweisprachig - deutsch-französisch - mit Simultanübersetzung.

Weitere Informationen zum Event finden Sie hier: https://www.unibas.ch/de/Aktuell/Veranstaltungen.html?id=e2aa9031-b2d0-49ca-a379-0b08b7f6759b

]]>Unlikely Double Intersections in a power of a modular curve

Tags: TAG Events DMI]]>

PDE-regularized learning

Tags: TAG Events DMI]]>

quantify the accuracy of the PDE model used for regularization and the data coverage.

Furthermore, the discretization of the PDE-regularized learning problem by generalized Galerkin methods including finite elements and neural networks approaches is investigated. A nonlinear version of Céa's lemma allows to derive errors bounds for both classes of discretizations and gives first insights into error analysis of variational neural network discretizations of PDEs.

For further information about the seminar, please visit this webpage.

]]>The intertwined derivative Schrödinger system of Calogero-Moser type. (Online Seminar via Zoom).]]>

Kolyvagin's Euler System and Heegner Points

Tags: TAG Events DMI]]>

Ih's conjecture and logarithmic equidistribution

Tags: TAG Events DMI]]>

Conforming Space-Time Finite Element Methods

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Das erste Event der neuen englischsprachigen Eventserie am DMI: "A slice of ...".

Tags: TAG Events DMI]]>

Beim ersten Event dieser Serien wird das Diversity & Inclusion Team einen spannenden Input geben. Das Event richtet sich an alle Angehörigen und Studierenden des DMI. Alle wichtigen Informationen stehen auch auf dem Poster.

Wenn Sie am Event teilnehmen möchten, dann füllen Sie bitte den "doodle" aus: https://xoyondo.com/dp/tzLuy4F5aBDv1Sx

]]>Singularities of a normal projective cubic surface

Tags: TAG Events DMI]]>

Harmonic Analysis meets Applications: Wavelet-based Function Spaces and Optimal Approximations of their Embeddings

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In this lecture, we first review the Fourier analytic approach towards by now well-established (Besov and Triebel-Lizorkin) scales of distribution spaces that measure either isotropic or dominating-mixed regularity. In addition, we introduce new function spaces of hybrid smoothness which are able to simultaneously capture both types of regularity at the same time. As a further generalization of the aforementioned scales, they particularly include standard Sobolev spaces on domains. On the other hand, our new spaces yield an appropri- ate framework to study break-of-scale embeddings by means of harmonic analysis. We shall present (non-)adaptive wavelet-based multiscale algorithms that approximate such embed- dings at optimal dimension-independent rates of convergence. Important special cases cover the approximation of functions having dominating-mixed Sobolev smoothness w.r.t. Lp in the norm of the (isotropic) energy space H1.

The talk is based on a recent paper [1] which represents the first part of a joint work with Glenn Byrenheid (FSU Jena), Markus Hansen (PU Marburg), and Janina Hübner (RU Bochum).

References:

[1] G. Byrenheid, J. Hübner, and M. Weimar. Rate-optimal sparse approximation of compact break-of-scale embeddings. Appl. Comput. Harmon. Anal. 65:40–66, 2023 (arXiv:2203.10011).

For further information about the seminar, please visit this webpage.

]]>12.10.2023 16:15, Spiegelgasse 5, Raum 05.002

Adaptive Spectral Inversion for Inverse Medium Problems

Tags: TAG Events Perlenkolloquium, TAG Events DMI]]>

Quantifying Domain Uncertainty in Linear Elasticity

Tags: TAG Events DMI]]>

A Kernel-based Multilevel Approximation Method for Higher-Dimensional Problems on Sparse Grids

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In machine learning, support vector machines heavily rely on RKHSs. For neural networks Barron spaces are connected to certain RKHSs and offer a possibility for a theoretical analysis of these networks.

Another application of RKHSs is in high(er)-dimensional approximation. For instance in the field of quasi Monte-Carlo methods, kernel-techniques are used to derive an error analysis for high-dimensional quadrature rules. We also developed a novel kernel-based approximation method for higher-dimensional meshfree function reconstruction, based on Smolyak operators.

In this talk I will provide an introduction into the theory of RKHSs, their kernels and associated kernel methods. In particular, I will focus on a multiscale approximation scheme for rescaled radial basis functions. This method will then be used to derive the new tensor product multilevel method for higher- dimensional meshfree approximation, which I will discuss in detail.

For further information about the seminar, please visit this webpage.

]]>Scale invariant bounds for mixing in the Rayleigh-Taylor instability

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Uniqueness of Radial Solutions of Nonlocal Elliptic Problems via ODE Method

Tags: TAG Events DMI]]>

Recent Advanced in Interacting particle methods for Bayesian Inference

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In this talk we present enhancement strategies of such ensemble methods based on sample enrichment and homotopy formalism, that ultimately lead to time-dependent drift terms that possible assimilate a larger class of target distributions while providing faster mixing times.

Furthermore, we present an alternative route to construct time-inhomogeneous drift terms based on reverse Diffusion processes that are popular in state-of-the-art Generative Modelling such as Diffusion maps. Here, we propose learning these log-densities by propagation of the target distribution through an Ornstein-Uhlenbeck process. For this, we solve the associated Hamilton-Jabobi-Bellman equation through an adaptive explicit Euler discretization using low-rank compression such as functional Tensor Trains for the spatial discretization.

For further information about the seminar, please visit this webpage.

]]>21.09.2023 16:15, Universität Basel Departement Mathematik und Informatik Seminarraum 05.002 (Spiegelgasse 5)

Embeddings and Automorphisms in Affine Algebraic Geometry

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Thereafter, we will focus on more general targets for algebraic embeddings, mainly linear algebraic groups.

]]>

The free energy of the dilute Bose gas]]>

While at temperature close to zero we have precise information on the ground state energy and the low-lying spectrum of excitations (at least in certain scaling limits), much less is known close to the critical point. In this talk I will discuss how thermal excitations can be described by Bogoliubov theory, allowing us to estimate the free energy of the Bose gas in the Gross-Pitaevskii regime.

This is joint work with A. Deuchert and D. Stocker.

]]>Vortrag von Prof. Dennis Komm (ETH Zürich)

Tags: TAG Events DMI]]>

Dennis Komm studierte Informatik und Psychologie an der RWTH Aachen sowie Informationstechnologie an der QUT Brisbane. Er promovierte 2012 an der ETH Zürich und arbeitete nach seiner Postdoc-Zeit an der ETH Zürich und anderen Hochschulen als Dozent und Senior Scientist. Ab 2021 war er Professor für Fachdidaktik Informatik an der PH Graubünden. Seit 2022 ist er ausserordentlicher Professor an der ETH Zürich für Algorithmen und Didaktik sowie Lehrgangsleiter des CAS Informatik und Informatikdidaktik für Lehrpersonen der Primar- und Sekundarstufe. Seine Forschungsinteressen sind der Entwurf und die Analyse von Algorithmen sowie die Informatikausbildung, speziell die Vermittlung von grundlegenden Ideen und Konzepten der Informatik.

]]>Zum Thema Big Data und Datenverwaltung für und mit Künstlicher Intelligenz

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Die Teilnehmerzahl ist begrenzt. Anmeldungen werden in der Reihenfolge des Eingangs berücksichtigt.

**Hier** können Sie sich anmelden.

Big Data, Machine Learning und künstliche Intelligenz gehören zu den Schwerpunkten von Professor Heiko Schuldt, vom Departement für Mathematik und Informatik der Universität Basel. Seine Forschungsgruppe entwickelt derzeit eine Multimedia-Suchmaschine, mit der man grosse Mengen an Bildern, Videos und 3d-Modellen mit neuartigen Methoden durchsuchen kann. Gemeinsam mit der Basler Firma 4eyes arbeiten die Wissenschaftlerinnen und Wissenschaftler an einer einer Anwendung, mit der multimediale Objekte in Museen und Archiven erschlossen werden können.

In einem anderen Projekt forscht das Team an einem neuartigen Datenbanksystem, mit dem Daten in komplett unterschiedlichen Formaten zusammen gespeichert und abgefragt werden können. Dieses Datenbanksystem wird derzeit mit einem Start-up unter dem Markennamen «Polypheny» kommerzialisiert.

Am Mittwoch, 28. Juni, bieten Heiko Schuldt und sein Team einen Einblick in ihre Arbeit. Erfahren Sie, wie die Erkenntnisse der Grundlagenforschung rasch in konkrete Projekte überführt werden und so Mehrwert für unsere Region geschaffen wird.

Werfen Sie im Rahmen von «Uni konkret» einen Blick in die Labors und diskutieren Sie mit den Forschenden. Im Video erfahren Sie mehr zum aktuellen Anlass.

__Programm__

Begrüssung

Referate

Q & A

Apéro

Ende der Veranstaltung

Zum Thema Big Data und Datenverwaltung für und mit Künstlicher Intelligenz

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Die Teilnehmerzahl ist begrenzt. Anmeldungen werden in der Reihenfolge des Eingangs berücksichtigt.

**Hier** können Sie sich anmelden.

Big Data, Machine Learning und künstliche Intelligenz gehören zu den Schwerpunkten von Professor Heiko Schuldt, vom Departement für Mathematik und Informatik der Universität Basel. Seine Forschungsgruppe entwickelt derzeit eine Multimedia-Suchmaschine, mit der man grosse Mengen an Bildern, Videos und 3d-Modellen mit neuartigen Methoden durchsuchen kann. Gemeinsam mit der Basler Firma 4eyes arbeiten die Wissenschaftlerinnen und Wissenschaftler an einer einer Anwendung, mit der multimediale Objekte in Museen und Archiven erschlossen werden können.

In einem anderen Projekt forscht das Team an einem neuartigen Datenbanksystem, mit dem Daten in komplett unterschiedlichen Formaten zusammen gespeichert und abgefragt werden können. Dieses Datenbanksystem wird derzeit mit einem Start-up unter dem Markennamen «Polypheny» kommerzialisiert.

Am Montag, 12. Juni, bieten Heiko Schuldt und sein Team einen Einblick in ihre Arbeit. Erfahren Sie, wie die Erkenntnisse der Grundlagenforschung rasch in konkrete Projekte überführt werden und so Mehrwert für unsere Region geschaffen wird.

Werfen Sie im Rahmen von «Uni konkret» einen Blick in die Labors und diskutieren Sie mit den Forschenden. Im Video erfahren Sie mehr zum aktuellen Anlass.

__Programm__

Begrüssung

Referate

Q & A

Apéro

Ende der Veranstaltung

Instantaneous loss of regularity for SQG with fractional diffusion

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Kolloquium des Forschungsnetzwerks Responsible Digital Society

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Fatos Ismali, Microsoft AI

__Abstract:__

“This session will provide an overview of the GPT-family of models, their architecture, training processes, various technical consideration to consider when deploying them for different business scenarios. It will also address the ethical challenges associated with AI-driven language models, including potential biases, content moderation, and data privacy and security. Lastly, the talk will explore the diverse use cases of GPT, highlighting its transformative impact on industries such as media, healthcare, customer service, and content creation. Join us as we unravel the intricacies of ChatGPT and discuss its potential to revolutionize human-AI interaction.”

__Curriculum Vitae:__

Fatos Ismali ist Senior Data & AI Solutions Architect bei Microsoft UK, wo er KI- und ML-Technologien einsetzt, um geschäftliche und gesellschaftliche Herausforderungen anzugehen. Vor seinem Eintritt bei Microsoft arbeitete er als Cloud Architect bei Oracle. In seiner aktuellen Rolle leitet Fatos die Task Force für Conversational AI und Cognitive Services und konzentriert sich darauf, grossen Unternehmen dabei zu helfen, KI und ML weitreichend einzusetzen. Er bietet Führungskräften auf C-Ebene, Chief Data Officers sowie Data- und AI-Architekten Beratung zur Erreichung von KI-Kompetenz, zur Schaffung funktionsübergreifender Data Science Teams und zur Entwicklung von KI-Fähigkeiten innerhalb von Microsofts Azure Cloud an.

Fatos hat mit führenden globalen Organisationen in verschiedenen Branchen zusammengearbeitet, darunter Finanzdienstleistern, Versicherungen, dem öffentlicher Sektor, Medien und Telekommunikation sowie Fertigung und Produkion. Im März 2020 erhielt er den Champions Award von Microsoft für seine bedeutenden Beiträge zum britischen NHS durch die Entwicklung der Datenanalyseplattform für das NHSX COVID-19 Test and Trace Programm. Im April 2023 erhielt Fatos seinen zweiten Champions Award für seine wegweisende Arbeit bei der Etablierung von Mustern für die Übernahme großer Sprachmodelle in der Telekommunikationsbranche unter Verwendung von Azure Open AI.

Mit großem Interesse an Natural Language Processing (NLP) und Machine Learning Operationalization (MLOps) trug Fatos zur MLOps-Architektur einer großen britischen Produktionsorganisation bei, die 2021 den DevOps Industry Award gewann.

Außerhalb von Microsoft gründete und leitet Fatos die Data Science Initiative Meetup-Community in London, die aus über 3.600 Data Scientists besteht. Diese Community fördert Zusammenarbeit und Wissensaustausch durch Präsentationen, Workshops und Hackathons. Als internationaler Sprecher präsentiert Fatos oft zu Themen wie MLOps, NLP, Cognitive AI und ML. Er hat einen Bachelor-Abschluss in Informatik und einen Master-Abschluss in Data Warehouses und Business Intelligence.

]]>Examples of non-uniqueness for the advection-diffusion equation

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

This is part of my Master's thesis, supervised by Massimo Sorella and Maria Colombo. ]]>

Gröbner Bases as a Tool in Cryptology

Tags: TAG Events DMI]]>

The strong Onsager conjecture

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

A new divisor in the moduli space of cubic fourfolds

Tags: TAG Events DMI]]>

Convergence of empirical Galerkin FEM for parametric PDEs with sparse TTs

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>«Privacy is dead, long live privacy!»

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Perlenkolloquium]]>

Wild solutions to Euler-Lagrange equations

Tags: TAG Events DMI]]>

Upper bounds on the ground state energy of dilute hard-core bosons

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We present a new upper bound for a dilute gas of hard core bosons in the thermodynamic limit, where the number of particles and the size of the box are sent to infinity while keeping the density fixed. Our result resolves the ground state energy up to an error of the order of the sub-leading correction. We also discuss the Gross-Pitaevskii regime, in which N hard spheres with radius of order 1/N move on the unit torus; in this setting, we show an upper bound for the energy, capturing the correct second order correction.

Based on joint works with G. Basti, A. Giuliani, A. Olgiati, G. Pasqualetti, B. Schlein. ]]>

Critical points of the Moser-Trudinger functional on closed surfaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

[in englischer Sprache] Auftakt CeDA Kolloquium

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Dr. Iain McGilchrist is a psychiatrist, neuroscientist, and philosopher best known for his books “The Master and His Emissary” and “The Matter With Things”. In these works, he compiles a wide body of research from science, philosophy and history, demonstrating that the two hemispheres of our brain have fundamentally different ways of attending to the world. He discusses the impact of this tension on our cultural evolution, as well as how it relates to epistemology and metaphysics. In this colloquium, Dr. McGilchrist will discuss the implications of his lateralization hypothesis on our approach to basic research, particularly in the life sciences. This will be followed by a round table discussion with Professor Cristina Granziera of the Department of Biomedical Engineering, and Professor Philipp Sterzer at the Psychiatric Hospital UPK.

Dr. McGilchrist will also be speaking in Geneva on May 8th at IdeaSquare (CERN) and May 9th at The Fab (the Graduate Institute).

]]>The cold-plasma model and simulation of wave propagation using B-Spline Finite Elements

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

This model has applications in magnetic confinement fusion devices, like the Tokamak. Namely, electromagnetic waves are used to heat up the plasma (Electron cyclotron resonance heating (ECRH)) or for interferometry and reflectometry diagnostics (to measure plasma density and position, etc.).

In the first part of this talk, we introduce the cold-plasma model, together with a qualitative study of the plasma modes which expose the complexity of the problem.

In the second part, we describe the problem and the simplifications we carry out, which yield the indefinite Helmholtz equation. It is solved with B-Spline Finite Elements provided by the Psydac library and some results are shown. Lastly, we discuss the performance and potential ways of preconditioning.

For further information about the seminar, please visit this webpage.

]]>Tags: TAG Events DMI]]>

Adaptive Coarse Space for Saddle Point problem

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Optimal test procedures for multiple hypotheses controlling the familywise expected loss

Tags: TAG Events DMI, TAG Events Perlenkolloquium, TAG Events Forschung Mathematik]]>

]]>

Traveling waves near shear flows

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

"Non-local" calculus for beginners

Tags: TAG Events DMI]]>

A least squares Hessian/Gradient recovery method for fully nonlinear PDEs in Hamilton–Jacobi–Bellman form (joint work wit Amireh Mousavi)

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

This idea allows the creation of efficient solvers for fully nonlinear elliptic equations, the linearization of which leaves us with an equation in nondivergence form. An important class of fully nonlinear elliptic PDEs can be written in Hamilton--Jacobi--Bellman (Dynamic Programming) form, i.e., as the supremum of a collection of linear operators acting on the unkown.

The least-squares FEM approach, a variant of the nonvariational finite element method, is based on gradient or Hessian recovery and allows the use of FEMs of arbitrary degree. The price to pay for using higher order FEMs is the loss of discrete-level monotonicity (maximum principle), which is valid for the PDE and crucial in proving the convergence of many degree one FEM and finite difference schemes.

Suitable functional spaces and penalties in the least-squares's cost functional must be carefully crafted in order to ensure stability and convergence of the scheme with a good approximation of the gradient (or Hessian) under the Cordes condition on the family of linear operators being optimized.

Furthermore, the nonlinear operator which is not necessarily everywhere differentiable, must be linearized in appropriate functional spaces using semismooth Newton or Howard's policy iteration method. A crucial contribution of our work, is the proof of convergence of the semismooth Newton method at the continuum level, i.e., on infinite dimesional functionals spaces. This allows an easy use of our non-monotone schemes which provides convergence rates as well as a posteriori error estimates.

For further information about the seminar, please visit this webpage.

]]>On the Kelvin-Voigt model for Viscoelastic material

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Kolloquium des Forschungsnetzwerks Responsible Digital Society

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Georges-Simon Ulrich, Direktor des Bundesamts für Statistik

__Zusätzliche Kurzpräsentationen__

Jonas Bieri, Bereichsleiter Daten- und Prozessmanagement beim Kanton Basel-Stadt**"Open Government Data for, with and from Reproducible Research"**

Silke Bellanger, Universitätsbibliothek Basel**"Research Data Management at the University of Basel"**

Im Anschluss an die Veranstaltung wird ein Apéro offeriert.

Es ist keine Anmeldung erforderlich.

Introduction to Full Waveform Inversion

Tags: TAG Events DMI]]>

High-dimensional kernel approximation of parametric PDEs over lattice point sets

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

References:

[1] V. Kaarnioja, Y. Kazashi, F. Y. Kuo, F. Nobile, and I. H. Sloan. Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification. Numer. Math. 150:33-77, 2022.

[2] V. Kaarnioja, F. Y. Kuo, and I. H. Sloan. Uncertainty quantification using periodic random variables. SIAM J. Numer. Anal. 58(2):1068-1091, 2020.

[3] V. Kaarnioja, F. Y. Kuo, and I. H. Sloan. Lattice-based kernel approximation and serendipitous weights for parametric PDEs in very high dimensions. Preprint 2023, arXiv:2303.17755 [math.NA].

For further information about the seminar, please visit this webpage.

]]>Of Mice and Men

Tags: TAG Events DMI]]>

Normalizing flows for density estimation and sampling

Tags: TAG Events DMI]]>

«Deep Learning for science and the science of Deep Learning?»

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Perlenkolloquium]]>

Regularity of the Pressure in the Incompressible Euler Equation in a Bounded Domain

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Kurzvorträge und Podiumsdiskussion

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik]]>

**17:00 Uhr Begrüssung**

**17:05 Präsentationen**

__Prof. Dr. Christine Alewell__, Departement Umweltwissenschaften, Universität Basel

“Big data for soil health assessment: from global erosion modelling to local remote mapping approaches”

__Prof. Dr. Giusi Moffa__, Departement Mathematik und Informatik, Universität Basel

“From real-world data to intervention effects: tales from the health sciences”

__Prof. Dr. Lukas Rosenthaler__, Digital Humanities Lab, Universität Basel

“The Digital Transformation in the Humanities - Open Data as an Opportunity for Culture and Society”

**18:00 Podiumsdiskussion: Open (Government) Data in Research**

Teilnehmende:

• Prof. Dr. Christine Alewell, Univ. Basel

• Jonas Bieri, Head of Data and Process Management beim Statistical Office des Kanton Basel-Stadt

• Prof. Dr. Giusi Moffa, Univ. Basel

• Prof. Dr. Lukas Rosenthaler, Univ. Basel

Moderation:

Andreas Amsler, ehemaliger Leiter Open Government Data Kanton Zürich

Im Anschluss an die Veranstaltung wird ein Apéro offeriert. Es ist keine Anmeldung erforderlich.

]]>Reconstructing the KdV Model from the Toda Chain by Inverse Scattering Transform

Tags: TAG Events DMI]]>

Towards robustness in shape optimization

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Das Angebot des Departements Mathematik und Informatik auf einen Blick

Tags: TAG Events DMI]]>

**Actuarial Science (Versicherungswissenschaft)****17.30 – 17.45 Uhr:** Präsentation Master Actuarial Science (Dr. Nils Rüfenacht)**17.45 – 18.30 Uhr:** offene Sprechstunde (Dr. Nils Rüfenacht, Dozent, und Jolanda Bucher, Studiengangleiterin)**18.30 – 19.00 Uhr:** Meet our Master Students

**Data Science****17.30 – 19.00 Uhr:** Präsentation Master Data Science (Prof. Ivan Dokmanić)**Anschliessend:** offene Sprechstunde (Dr. Sabine Meinel, Studiengangkoordinatorin)

**Informatik (Computer Science)****17.30 – 19.00 Uhr:** Präsentation Master Informatik / Computer Science (Prof. Heiko Schuldt)**Anschliessend:** offene Sprechstunde (Dr. Heike Freiberger, Studiengangkoordinatorin)

**Mathematik****17:30 – 19:00 Uhr:** Vorstellung der Vertiefungsmodule Master (Einleitung von Prof. Enno Lenzmann, Vertiefung durch Prof. Jiří Černý, Prof. Gianluca Crippa, Prof. Marcus Grote, Prof. Philipp Habegger)**Anschliessend:** offene Sprechstunde (Heidi Karypidis, Studiengangkoordination)

Um **Anmeldung** wird gebeten.

Einwahl während des Programms jederzeit möglich.

Weitere Informationen zum Angebot anderer Studiengänge finden Sie **hier**.

The Dirac equation in dispersive PDEs: advances and open problems]]>

Vortrag von Prof. Dr. Philipp Habegger im Rahmen der Vortragsreihe «Behind the science»

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Wir laden Euch zu einem Vortrag von Prof. Dr. Philipp Habegger, Inhaber des Lehrstuhls für Zahlentheorie an der Universität Basel, ein, bei dem wir uns auf eine abenteuerliche Reise ins Reich der Zahlen begeben. Und Kuchen gibt es natürlich auch!

Moderation: Prof. Dr. Botond Roska, leitender Direktor des IOB

Die Teilnahme ist kostenlos. Meldet Euch jetzt **hier** an!

Bitte beachtet, dass der Anlass auf Englisch stattfindet und dass die Anzahl freier Sitzplätze begrenzt ist.

Runge-Kutta Based Local Time-Stepping Methods for Forced Wave Equations

Tags: TAG Events DMI]]>

Non selection of vanishing viscositysolutions to the advection equation

Tags: TAG Events DMI]]>

Tags: TAG Events DMI]]>

]]>

Invariant KAM tori for the planar Euler equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

«An optimization perspective on Deep Learning»

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Perlenkolloquium]]>

Im Anschluss an die Vorlesung wird ein Apéro offeriert.

]]>Derivation of the Vlasov equation for singular interactions]]>

old problem in

mathematical physics. But while the most interesting interactions in

nature have singularities,

one typically assumes some Lipschitz condition on the interaction

force for its microscopic

derivation. Recent developments have given results, where the

interaction force gets singular

when the particle number N tends to infinity, usually by mollifying

or cutting the singularity

with a N-dependent mollifier or cut-off parameter.

In the talk I will present most recent developments and new results on

this topic. ]]>

Öffentliche Veranstaltung mit anschliessendem Apéro

Tags: TAG Events DMI]]>

Eine Absolventin und ein Absolvent des Masterstudiengangs Actuarial Science, Claudia Theiler und Thom van Rijn, werden ihre Masterarbeiten vorstellen und Dr. Harald Dornheim (PwC Schweiz) wird diese mit seinen Erfahrungen aus der Praxis ergänzen.

Im Anschluss gibt es einen Apéro. Das ist eine gute Gelegenheit, Studienkolleg:innen und Dozent:innen wiederzusehen und sich mit anderen Aktuar:innen auszutauschen.

Alle Interessierten sind herzlich eingeladen. Für die Vorträge und den anschliessenden Apéro ist keine Anmeldung erforderlich. Der Besuch der Veranstaltung ist von der SAV als Weiterbildung anerkannt (1 SAV-CP).

**Anmeldung AlumniEssen**

Das AlumniEssen findet im Restaurant *Zum Isaak* statt und ist für Mitglieder von AlumniActuarialScience und solche, die es gerne werden wollen. Bitte anmelden bis am 30. Januar 2023: info@AlumniActuarialScience.ch.

Prof. Dr. Gianluca Crippa: Anomalous dissipation in fluid dynamics

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Perlenkolloquium]]>

Workshop for researchers, software builders and members of the SSB community to study the properties and potential of Secure Scuttlebutt

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

For more information, please visit the**event website**.

Die 22. Ausgabe der Basler Museumsnacht

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Die DBIS Forschungsgruppe zeigt das «Virtual Museum» im Historischen Museum Basel (HBM) in der Barfüsserkirche. Von 18:00 Uhr - 02:00 Uhr können Besucherinnen und Besucher ihre eigene virtuelle HMB-Ausstellung zusammenstellen.

Weitere Informationen zum Programm finden Sie auf der **Webseite der Museumsnacht**.

Singular Stochastic PDEs

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

∂_{t}u = △u + F (u, ∂_{x}u, ξ),

where ξ is an irregular driving noise, arise in a variety of situations from quantum field theory to probability. After introducing some specific examples, we describe the main difficulty they share; they are singular due to the irregularity of the driving noise ξ.

In the first part of the talk we discuss a simple example where using the so-called “Da Prato-Debusche trick” is sufficient to deal with this difficulty. In the second half, we give a birds-eye view on how regularity structures provide a solution theory for such equations. In particular, we explain the role of subcriticality (super-renormalisability) and (half) Feynman diagrams in this theory. Lastly, we shall mention some recent results on the class of differential operators that are compatible with this general machinery and how this relates to the geometry of the underlying space.

]]>Stability and Construction of hyperbolic metrics in dimension 3

Tags: TAG Events DMI]]>

Kolloquium von Prof. Henning Müller mit anschliessendem Apéro

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

This presentation will summarize the main work done in the research group of Henning Müller at the HES-SO Valais in Sierre on medical multimodal data analysis. This work ranges from image creation differences, to biomarker extraction from radiology and histopathology images towards clinical decision support. An essential part of integrating the mainly deep learning based approaches is to be able to explain decisions and predictions, whereas deep learning networks are usually black boxes.

All these aspects can help to create a digital view on patients where several options for prevention or treatment can be adapted interactively. This is also name digital twins in industry and is a concept that we expect to become more common in the medical field when longitudinal data on patients is available.

__Biography:__

Henning Müller studied medical informatics at the University of Heidelberg, Germany, then worked at Daimler-Benz research in Portland, OR, USA. From 1998-2002 he worked on his PhD degree in computer vision at the University of Geneva, Switzerland with a research stay at Monash University, Melbourne, Australia. Since 2002, Henning has been working for the medical informatics service at the University Hospital of Geneva. Since 2007, he has been a full professor at the HES-SO Valais and since 2011 he is responsible for the eHealth unit of the school. Since 2014, he is also professor at the medical faculty of the University of Geneva. In 2015/2016 he was on sabbatical at the Martinos Center, part of Harvard Medical School in Boston, MA, USA to focus on research activities. Henning is coordinator of the ExaMode EU project, was coordinator of the Khresmoi EU project, scientific coordinator of the VISCERAL EU project. Since early 2020 he is also a member of the Swiss National Research Council.

]]>Non-reflecting boundary conditions and domain decomposition methods for industrial flow acoustics

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

[1] Marchner, P., Antoine, X., Geuzaine, C., & Bériot, H. (2022). Construction and numerical assessment of local absorbing boundary conditions for heterogeneous time-harmonic acoustic problems. SIAM Journal on Applied Mathematics, 82(2), 476-501.

[2] Lieu, A., Marchner, P., Gabard, G., Beriot, H., Antoine, X., & Geuzaine, C. (2020). A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics. Computer Methods in Applied Mechanics and Engineering, 369, 113223.

For further information about the seminar, please visit this webpage.

]]>Introduction to real del Pezzo surfaces

Tags: TAG Events DMI]]>

T-coercivity: a practical tool for the study of variational formulations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In this talk, I will focus on an approach that is completely equivalent to the inf-sup condition for problems set in Hilbert spaces, the **T-coercivity approach**. This approach relies on the design of an *explicit* operator to realize the inf-sup condition. If the operator is carefully chosen, it can provide useful insight for a straightforward definition of the approximation of the exact problem. As a matter of fact, the derivation of the discrete inf-sup condition often becomes elementary, at least when one considers conforming methods, that is when the discrete spaces are subspaces of the exact Hilbert spaces. In this way, both the exact and the approximate problems are considered, analysed and solved at once.

In itself, T-coercivity is not a new theory, however it seems that some of its strengths have been overlooked, and that, if used properly, it can be a simple, yet powerful tool to analyse and solve linear PDEs. In particular, it provides guidelines such as, which abstract tools and which numerical methods are the most “natural” to analyse and solve the problem at hand. In other words, it allows one to select simply appropriate tools in the mathematical, or numerical, toolboxes. This claim will be illustrated on classical linear PDEs, and for some generalizations of those models.

For further information about the seminar, please visit this webpage.

]]>A strong Onsager conjecture on the Euler equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Self-Avoiding Walks and Parafermionic Observables

Tags: TAG Events DMI]]>

Mathematical analysis of stably stratified fluids

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Sign of eigenfunctions

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Stabilisation — using a multiplier strategy — of spurious high frequencies for high-order discretisations of the wave equation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Long-time behaviour in the 2D Euler-Boussinesq equations near a stably stratified Couette flow

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Introduction to BEM and H-matrices

Tags: TAG Events DMI]]>

On analytic and Gevrey class regularity for parametric elliptic eigenvalue problems (A. Chernov, T. Le)

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Informiere dich über das vielfältige und umfangreiche Studienangebot der Universität Basel

Tags: TAG Events DMI]]>

Gestalte deinen Tag ganz individuell und stelle dir anhand des **Programms** deinen Tag zusammen.

Some probabilistic approaches for NLS in the Euclidean space

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Feature Allocation Approach for Multimorbidity Trajectory Modelling

Tags: TAG Events DMI]]>

Kolloquium von Jacqueline Staub (Universität Trier)

Tags: TAG Events DMI]]>

Jacqueline Staub ist eine Schweizer Informatikerin, die international bekannt ist für die Leitung in der Entwicklung der pädagogischen Programmierumgebung "XLogoOnline". Diese Umgebung ermöglicht einen durchgängigen Programmierunterricht vom Kindergarten bis zum Abitur. Jacqueline Staub hat nach Bachelor, Master und Doktorat in Informatik an der ETH Zürich sowie einem Lehrdiplom für Informatik den Ruf an die Universität Trier erhalten, wo sie seit Januar 2022 die CZS Stiftungsprofessur für Informatik und ihre Didaktik leitet.

]]>

Transport of currents and geometric Rademacher-type theorems

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Simulation of the Stochastic Heat Equation on the Sphere

Tags: TAG Events DMI]]>

Determination of a learnt best basis for two geoscientific inverse problems

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Traditionally, an approximation of such a linear(ized) inverse problem is obtained in one, a-priori chosen basis system: either a global one, e.g. spherical harmonics or polynomials on the ball, or a local one, e.g. radial basis functions and wavelets on the sphere or finite elements on the ball.

In the Geomathematics Group Siegen, we developed methods that enable us to combine different types of trial functions for such an approximation. The idea is to make the most of the benefits of different types of available trial functions. The algorithms are called the (Learning) Inverse Problem Matching Pursuits (LIPMPs). They construct an approximation iteratively from an intentionally overcomplete set of trial functions, the dictionary, such that the Tikhonov functional is reduced. Due to the learning add-on, the dictionary can very well be infinite. Moreover, the computational costs are usually decreased.

In this talk, we give details on the LIPMPs and show some current numerical results.

For further information about the seminar, please visit this webpage.

]]>Öffentliche Vortragsreihe

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Nähere Inforationen zur Vortragsreihe sowie zur Anmeldung finden Sie auf der **Webseite der Volkshochschule Beider Basel**.

A gentle introduction to the Schinzel-Zassenhaus conjecture and its proof

Tags: TAG Events DMI]]>

Internationales Symposium zum Abschluss der gedruckten Euler-Edition

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Zum Abschluss der gedruckten Edition der Opera Omnia organisiert die Bernoulli-Euler-Gesellschaft zusammen mit der Plattform Mathematik, Astronomie und Physik der SCNAT ein internationales Symposium am 29. Oktober 2022 in Basel.

Dies ist gleichzeitig auch die Überleitung in eine neue Phase: Alle Werke, Briefe und Notizbücher von Euler, den Bernoulli und deren Umfeld sollen auf einer modernen digitalen Plattform online und frei zugänglich präsentiert werden.

- 14.30 Uhr: Prof. Dr. Umberto Bottazzini (Università degli Studi di Milano): «Elastica, Lemnicate and Euler's Addition Theorem for Elliptic Integrals»
- 15.30 Uhr: Prof. Dr. Jesper Lützen (University of Copenhagen): «Euler’s general Analysis versus Applications»
- 16.30 Uhr: Kaffeepause
- 17.00 Uhr: Prof. Dr. Helmut Pulte (Ruhr-Universität Bochum): «Euler's Philosophy of Space and Time. With a Note on its Reception by Kant»

Im Vorfeld des Symposiums findet am 28. Oktober auch eine Jubiläumsfeier zum Abschluss der gedruckten Euler-Edition statt.

]]>Jubiläumsfeier zum Abschluss der gedruckten Euler-Edition

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Zum Abschluss der gedruckten Edition der Opera Omnia organisiert die Bernoulli-Euler-Gesellschaft zusammen mit der Plattform Mathematik, Astronomie und Physik der SCNAT eine Jubiläumsfeier am 28. und 29. Oktober 2022 in Basel.

Dies ist gleichzeitig auch die Überleitung in eine neue Phase: Alle Werke, Briefe und Notizbücher von Euler, den Bernoulli und deren Umfeld sollen auf einer modernen digitalen Plattform online und frei zugänglich präsentiert werden.

**Freitag, 28. Oktober 2022**

**In der Aula im Kollegienhaus der Universität, Petersplatz 1**

- 17:00 Uhr: Grussworte von Prof. Dr. Andrea Schenker-Wicki, Rektorin der Universität Basel; Prof. Dr. Marcel Tanner, Präsident der Akademien der Wissenschaften Schweiz; Prof. Dr. Matthias Egger, Präsident des Stiftungsrates des Schweizerischen Nationalfonds
- 17:30 Uhr: Festvortrag von Prof. Dr. Günter Ziegler, Präsident der Freien Universität Berlin: «Mathematik, ein weites Feld. Euler als Universalist»
- 18:30 Uhr: Apéro und Vernissage des Bandes II 27 zur Himmelsmechanik und Präsentation des Euler-Comic

**Samstag****, 29. Oktober 2022**

**Im grossen Hörsaal der alten Universität, Rheinsprung 9**

- 09:00 Uhr: Türöffnung, Kaffee und Tee
- 10:00 Uhr: Prof. Dr. Hans-Christoph Im Hof (Basel): «Die Edition der Werke Leonhard Eulers», Prof. Dr. Andreas Kleinert (Halle): «Von den Petersburger Manuskripten zur Series IVA der Opera omnia. Zur Geschichte der Euler-Briefedition»
- 11:30 Uhr: PD Dr. Rita Gautschy (Basel) und Prof. Dr. Gerd Grasshoff (Berlin): «Opera-Bernoulli-Euler.digital», mit Demonstrationen (bitte eigenes Notebook mitbringen!)

Neben der Jubiläumsfeier findet am 29. Oktober auch ein internationales Symposium zum Abschluss der gedruckten Euler-Edition statt.

]]>The Plateau problem and currents

Tags: TAG Events DMI]]>

The positive mass conjecture

Tags: TAG Events DMI]]>

Sparse grid approximation of the Riccati operator

Tags: TAG Events DMI]]>

Counting Torsion Points on Algebraic Subvarieties of the Algebraic Torus

Tags: TAG Events DMI]]>

Modelling Progressive Disease

Tags: TAG Events DMI]]>

Infoveranstaltung für Bachelor-Studierende der Mathematik und der Informatik

Tags: TAG Events DMI]]>

- Informationen rund um das Studium durch Prof. Malte Helmert (Informatik) und Prof. Philipp Habegger (Mathematik)
- Kennenlernen der anderen Erstsemestrigen und der «höheren Semester»
- die Fachgruppe Mathematik und Informatik (FMI) stellt sich vor
- Zeit für Ihre Fragen
- kurzer Rundgang mit der Fachgruppe zu den für Sie wichtigen Gebäuden der Uni
- Abschluss: Treffen im Zwischengeschoss DMI zum Plaudern bei einem kleinen Apéro

Infoveranstaltung für Master-Studierende der Informatik

Tags: TAG Events DMI]]>

Studierende berichten live aus ihrem Studienalltag

Tags: TAG Events DMI]]>

Für kurzfristige Änderungen sichten Sie bitte die Webseite der Studienberatung Basel.

]]>Die 21. IEEE ISPDC-Konferenz wird von der Universität Basel ausgerichtet und in Basel stattfinden

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

]]>

Der ICM findet in diesem Jahr als vollständig virtuelle Veranstaltung statt

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

- Die Vorlesungen finden täglich zwischen 9:00 und 18:00 Uhr MESZ statt.
- Am 6. Juli werden die Fields-Medaillengewinner 2022 und die IMU Abacus-Medaillengewinner Preisträgervorträge live in Helsinki halten. Die Vorträge sind öffentlich und werden live gestreamt.
- Die Teilnahme am ICM 2022 ist kostenlos, eine Anmeldung ist jedoch erforderlich.

Weitere Ankündigungen erfolgen auf der ICM 2022-Webseite.

**Wenn Sie am ICM 2022 teilnehmen möchten, melden Sie sich bitte hier an**.

Effective Dynamics of Extended Fermi Gases at High Density]]>

volume

$\Lambda$. We show that, in the high-density regime and for zero-temperature

initial data

exhibiting a local semiclassical structure, the solution of the many-body

Schrödinger equation can be approximated by the solution of the nonlinear

Hartree equation, up to errors that are small, for large density, uniformly

in $N$ and $\Lambda$. This is joint work with M. Porta and B. Schlein.

]]>

Bose-Einstein condensation in the Kompaneets equation

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

boundary. This degeneracy, combined with the nonlinearity causes an out-flux of photons with zero energy, often interpreted as a Bose-Einstein condensate. This talk will describe several results about the long time behavior of these equations including convergence to equilibrium,

persistence of the condensate, sufficient conditions under which it forms, sufficient conditions under which it doesn't form and a loss formula for the mass of the condensate. ]]>

Global existence for the 2D Kuramoto-Sivashinsky equation with growing modes

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Dividing a set in half

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Given a set E in R^d with finite volume, is it possible to find an hyperplane P that cuts E in two parts with equal volume, and such that the area of the cut (that is, the intersection of P and E) is of the expected order, namely (vol(E))^{1−1/d}?

We can show that this question, even in a stronger form, has a positive answer if the dimension d is 3 or higher.But, interestingly enough, our proof breaks down completely in dimension d=2, and we do not know the answer in this case (but we know that the answer is positive if we allow cuts that are not exactly planar, but close to planar). It turns out that this question has some interesting connection with the Kakeya problem.

This is a work in progress with Alan Chang (Princeton University). ]]>

Some fun ideas from differential topology in algebraic geometry

Tags: TAG Events DMI]]>

26.05.2022 17:00 - 26.05.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Applications of arithmetic holonomicity theorems

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

This is joint work with Frank Calegari and Vesselin Dimitrov.

For further information about the seminar, please visit this webpage.

]]>Die FANTASY BASEL – The Swiss Comic Con ist zurück!

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Weitere Informationen zur Messe finden Sie hier:

]]>2D incompressible Euler system in presence of sources and sinks

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The old man and the sea

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Diesmal findet die Museumsnacht Basel im Mai statt!

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Weitere Informationen zum Programm finden Sie hier:

]]>Riccati-Feedback Stabilization of Optimal Control Problems with PDE Constraints

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

On the other hand, the linear-quadratic regulator problem in system theory is an approach to make a dynamical system react to perturbation via feedback controls that can be expressed by the solutions of matrix Riccati equations. It’s applicability is limited by the linearity of the dynamical system and the efficient solvability of the quadratic matrix equation.

In this talk, we discuss how certain classes of non-stationary PDEs can be reformulated (after spatial semi-discretization) into structured linear dynamical systems that allow the Riccati feedback to be computed. This allows us to combine both approaches and thus steer solutions of perturbed PDEs back to the optimized trajectories. The key to efficient solvers for the Riccati equations is the usage of the specific structure in the problems and the fact that the Riccati solutions usually feature a strong singular value decay, and thus good low-rank approximability.

For further information about the seminar, please visit this webpage.

]]>19.05.2022 17:00 - 19.05.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Schinzel's determinant inequality and a conjecture of F. Rodriguez Villegas

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Pointwise description of Eulerian vector fields and rotational properties of their flows

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Universal equations for isotropic Grassmannians

Tags: TAG Events DMI]]>

]]>

12.05.2022 17:00 - 12.05.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Generalizations of the Montgomery-Hooley asymptotic formula; A survey.

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>“We are Computer Science” is pleased to invite you to attend the talk given by Dr. Nataliia Rzhevska

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

cognitive future for students while supporting teachers at university level.

In her work, she aims at strengthening civil society structures and empowerment in the areas of research and gender equality as well as information and knowledge management. Nataliia is also CIO of VideoWiki, a collaborative platform for learners and educators to secure earning continuity in times of restrictions and beyond.

The event will be held on on Zoom. If you are interested, please contact us, to get the link to join (info.we-are-cs@*clutter*unibas.ch).

The Aufbau principle in the Theory of Operators

Tags: TAG Events DMI]]>

05.05.2022 17:00 - 05.05.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

On integers which are(n't) the sum of two rational cubes

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

I will explain joint work with Bhargava and Shnidman in which we show:

1. At least a sixth of integers are not the sum of two rational cubes,

and

2. At least a sixth of odd integers are the sum of two rational cubes!

(--- with 2. relying on new 2-converse results of Burungale-Skinner.)

The basic principle is that "there aren't even enough 2-Selmer elements to go around" to contradict e.g. 1., and we show this by using the circle method "inside" the usual geometry of numbers argument applied to a particular coregular representation. Even then the resulting constant isn't small enough to conclude 1., so we use the clean form of root numbers in the family x^3 + y^3 = n and the p-parity theorem of Nekovar/Dokchitser-Dokchitser to succeed.

For further information about the seminar, please visit this webpage.

]]>Genericity of non-Lagrangian solutions to the transport equation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Complete Blow-up in Reaction-Diffusion Equations

Tags: TAG Events DMI]]>

28.04.2022 17:00 - 28.04.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Linear Divisibility sequences

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

In a sequence of papers in the 1930s, Marshall Hall further developed several of Lucas' themes, including studying and trying to classify third order linear divisibility sequences; that is, linear recurrences like the Fibonacci numbers which have the additional property that $F_m$ divides $F_n$ whenever $m$ divides $n$. Because of many special cases, Hall was unable to even conjecture what a general theorem should look like, and despite developments over the years by various authors, such as Lehmer, Morgan Ward, van der Poorten, Bezivin, Petho, Richard Guy, Hugh Williams,... with higher order linear divisibility sequences, even the formulation of the classification has remained mysterious.

In this talk we present our ongoing efforts to classify all linear divisibility sequences, the key new input coming from a wonderful application of the Schmidt/Schlickewei subspace theorem from the theory of diophantine approximation, due to Corvaja and Zannier.

For further information about the seminar, please visit this webpage.

]]>Evening event with apéro

Tags: TAG Events DMI]]>

We invite you to the new seminar “Bernoulli meets Industry”, an evening event where

former mathematicians talk about their current work, followed by an apéro.

]]>Existence of non-radial stationary solutions to the 2D Euler equation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

A positivity-preserving numerical scheme for stochastic heat equations with multiplicative space-time white noise

Tags: TAG Events DMI]]>

Structure-Preserving Model Reduction for Symmetric Second-Order Systems

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Our method guarantees to preserve passivity of the reduced-order model as well as the positive definiteness of the mass and stiffness matrices and admits an a priori gap metric error bound.

Our construction of the second-order reduced model is based on the consideration of an internal symmetry structure and the invariant zeros of the system and their sign-characteristics for which we derive a normal form.

The results are available in [1].

[1] I. Dorschky, T. Reis, and M. Voigt. Balanced truncation model reduction for symmetric second order systems - a passivity-based approach. SIAM J. Matrix Anal. Appl., 42(4):1602--1635, 2021.

For further information about the seminar, please visit this webpage.

]]>21.04.2022 17:00 - 21.04.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Short exponential sums of the primes

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>14.04.2022 17:00 - 14.04.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Probability Theory and the Riemann Hypothesis

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>MacWilliams’ Extension Theorem for rank-metric codes

Tags: TAG Events DMI]]>

Adaptive Approximation of Shapes

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>07.04.2022 17:00 - 07.04.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

On the cohomology of Shimura varieties with torsion coefficients

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>]]>

Slice knots - knot theory in dimension 4

Tags: TAG Events DMI]]>

Introduction to finite element error estimates for optimal control problems with PDEs

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>31.03.2022 17:00 - 31.03.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Markoff triples and connectivity of Hurwitz spaces

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Exponential convergence rate in the approximation of analytic functions by deep neural networks

Tags: TAG Events DMI]]>

Combined iterative methods for solving nonlinear equations with nondifferentiable operators

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The local and semi-local convergence of the proposed methods is studied and the order of their convergence is established. We apply our results to the numerical solving of systems of nonlinear equations.

For further information about the seminar, please visit this webpage.

]]>24.03.2022 17:00 - 24.03.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Group based zeta functions

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Rigorous validity of the Choh-Uhlenbeck equation ]]>

∂tfϵ=Qϵ,BE(fϵ,fϵ)+ϵQϵ,CU(fϵ,fϵ,fϵ).

Here Qϵ,BE is the Boltzmann-Enskog operator, and the Choh-Uhlenbeck operator Qϵ,CU is an explicit cubic operator. This operator accounts for the formation of dynamic microscopic correlations between three particles. In this work, we prove rigorously that the Choh-Uhlenbeck equation gives the first order correction to the Boltzmann equation in the Grad-scaling. This is a joint work with Sergio Simonella.

Multivariate Cryptography

Tags: TAG Events DMI]]>

Optimality of adaptive stochastic Galerkin methods for affine-parametric elliptic PDEs

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

M. Bachmayr and I. Voulis, *An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality*, arXiv:2109:09136

For further information about the seminar, please visit this webpage.

]]>Tags: TAG Events DMI]]>

Hier finden Sie die Angebote des Departement Mathematik und Informatik:

**Präsentation und offene Sprechstunde haben jeweils den selben Zoom-Link.***Die Zoom-Meetings sind durchgehend geöffnet, sodass vor und nach den Präsentationen Fragen gestellt werden können.*

**Actuarial Science **

https://unibas.zoom.us/j/68772491742

**17:30-18:15** Präsentation Master Actuarial Science und offene Sprechstunde**18:30-19:15** Meet our Students**19:30-20:00** Präsentation Master Actuarial Science und offene Sprechstunde

Testimonial der Masterstudentin Claudia Theiler: https://www.youtube.com/watch?v=TJ70E1V-nwc

HIER finden Sie eine Übersichtpräsentation zum Masterstudiengang Actuarial Science.

**Computer Science**

https://unibas.zoom.us/j/67965624099

**19:30-20:00 **Präsentation Master Computer Science**17:30-20:00** Offene Sprechstunde

HIER finden Sie eine Übersichtspräsentation zum Masterstudiengang Computer Science.

**Data Science **

https://unibas.zoom.us/j/62557326301

**18:00-19:00** Präsentation Master Data Science und offene Sprechstunde

HIER finden Sie eine Übersichtpräsentation zum Masterstudiengang Data Science.

**Mathematik **

https://unibas.zoom.us/j/64257789993

**18:30-19:15** Präsentation der Vertiefungsmodule HS22/FS23**17:30-20:00** Offene Sprechstunde

HIER finden Sie eine Übersichtpräsentation zum Masterstudiengang Mathematik.

]]>17.03.2022 17:00 - 17.03.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Diophantine Approximation for Closed Subschemes

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>How Do Oil And Water Interact?

Tags: TAG Events DMI]]>

10.03.2022 17:00 - 10.03.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>03.03.2022 17:00 - 03.03.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Modular Curves and Asymptotic Solutions to Fermat-type Equations

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Obtaining quantitative hypocoercivity estimates by using Harris-type theorems.]]>

Action of polynomial automorphisms on valuation spaces

Tags: TAG Events DMI]]>

Dr. Manuela Moor: Research coordinator and data scientist

Tags: TAG Events DMI]]>

We invite you to the new seminar “Bernoulli meets Industry”, an evening event where

former mathematicians talk about their current work, followed by an apéro.

Regarding Covid: This event will take place in accordance with the university regulations.

If you want to participate, please register under the following link:

*UPDATE: Due to the current situation, the talk is open for everyone.*

]]>24.02.2022 17:00 - 24.02.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Sums of Kloosterman and Salie Sums and Moments of L-functions

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>17.02.2022 17:00 - 17.02.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Counting rational points and lower bounds for Galois orbits for special points on Shimura varieties

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>10.02.2022 17:00 - 10.02.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Beyond uniform distribution

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Zahlentheorie]]>

For further information about the seminar, please visit this webpage.

]]>03.02.2022 17:00 - 03.02.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

L^p-norm bounds for automorphic forms

Tags: TAG Events DMI, TAG Events Zahlentheorie, TAG Events Forschung Mathematik]]>

For further information about the seminar, please visit this webpage.

]]>27.01.2022 17:00 - 27.01.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Reflections on the proof(s) of the Vinogradov mean value conjecture

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Outlier detection for shape model fitting

Tags: TAG Events Forschung Informatik, TAG Events DMI]]>

The defence will take place on Zoom. (The meeting ID was sent via email).

]]>20.01.2022 17:00, Zoom: register here: https://www.ntwebseminar.org/

Rank of matrices with entries from a multiplicative group

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Zahlentheorie]]>

For further information about the seminar, please visit this webpage.

]]>13.01.2022 17:00 - 13.01.2022 18:00, Zoom: register here: https://www.ntwebseminar.org/

Irreducibility of random polynomials

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Zahlentheorie]]>

For further information about the seminar, please visit this webpage.

]]>13.01.2022 11:00 - 13.01.2022 15:30, Zoom

Tags: TAG Events DMI, TAG Events Studium Mathematik, TAG Events Studium Informatik]]>

Weitere Informationen sowie Links zu den einzelnen Veranstaltungen finden Sie auf der Seite der Universität Basel.

]]>21.12.2021 12:00 - 21.12.2021 14:00

Die Informationsveranstaltung zum Thema Bachelorarbeit Bachelor Computer Science findet am Dienstag, 21.12.21 12.00 - 14.00 Uhr im Raum HS U1.141 im Neuen Biozentrum und per Zoom statt.

Tags: TAG Events Studium Informatik, TAG Events DMI]]>

Wo: Raum HS U1.141 im Neuen Biozentrum und per Zoom (Zoomlink folgt per Email)

Themen:

- Ablauf der Arbeit
- Bachelorarbeitsthemen der einzelnen Forschungsgruppen

First Order Operators On Spacetimes With Timelike Boundary

Tags: TAG Events DMI]]>

Some results on Perfectly Matched Layers (PML) for non-dispersive and dispersive Maxwell’s equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In this talk, we address the questions of well-posedness, stability and convergence of standard and new models of PMLs in the context of electromagnetic waves for non-dispersive and dispersive materials.

For further information about the seminar, please visit this webpage.

]]>16.12.2021 17:00 - 16.12.2021 18:00, Zoom: register here: https://www.ntwebseminar.org/

Euler systems and the Birch—Swinnerton-Dyer conjecture for abelian surfaces

Tags: TAG Events Zahlentheorie, TAG Events DMI, TAG Events Forschung Mathematik]]>

I will recall a series of recent works (variously joint with Loeffler, Pilloni, Skinner) giving rise to an Euler system in the cohomology of Shimura varieties for GSp(4), and an explicit reciprocity law relating the Euler system to values of L-functions. I will then recent work with Loeffler, in which we use this Euler system to prove new cases of the BSD conjecture for modular abelian surfaces over Q, and modular elliptic curves over imaginary quadratic fields.

For further information about the seminar, please visit this webpage.

]]>Quasisymmetric uniformization

Tags: TAG Events DMI]]>

Residual and restarting in Krylov subspace evaluation of the φ function

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>09.12.2021 17:00 - 08.12.2021 18:00, Zoom: register here: https://www.ntwebseminar.org/

The Fermat equation and the unit equation

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Zahlentheorie]]>

For further information about the seminar, please visit this webpage.

]]>Mixing properties of BV vector fields

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

1) weakly mixing vector fields are a residual G_delta-set in U;

2) (exponentially fast) strongly mixing vector fields are a dense subset of U.

The proof of these results exploits some connections between ergodic theory and fluid dynamics and it is based on the density of BV vector fields whose Regular Lagrangian Flow is a permutation of subsquares of the unit square [0,1]^2 when evaluated at time t=1.

]]>Double machine learning in partially linear models

Tags: TAG Events DMI]]>

Adaptive algorithms for solution of an electromagnetic volume integral equation with application to microwave thermometry

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Based on these estimates, different adaptive finite element algorithms are formulated. Numerical examples will show efficiency of the proposed adaptive algorithms to improve quality of 3D reconstruction of target during the process of microwave thermometry which is used in cancer therapies. This is joint work with the group of Biomedical Imaging at the Department of Electrical Engineering at CTH, Chalmers.

For further information about the seminar, please visit this webpage.

]]>02.12.2021 17:00 - 02.12.2021 18:00, Zoom: register here: https://www.ntwebseminar.org/

Orders of abelian varieties over $\mathbb{F}_2$

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Zahlentheorie]]>

For further information about the seminar, please visit this webpage.

]]>Nonuniqueness results for the 2d Euler equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Braess, Simpson, and Zorn

Tags: TAG Events DMI]]>

25.11.2021 17:00 - 25.11.2021 18:00, Zoom: register here: https://www.ntwebseminar.org/

On uniformity conjectures for abelian varieties and K3 surfaces

Tags: TAG Events Zahlentheorie, TAG Events DMI, TAG Events Forschung Mathematik]]>

For further information about the seminar, please visit this webpage.

]]>The isoperimetric problem on spaces with curvature bounded from below

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

When the space is compact, the existence of isoperimetric regions for every volume is established through a simple application of the direct method of Calculus of Variations. In the noncompact case, part of the mass could be lost at infinity in the minimization process. Such a mass can be recovered in isoperimetric regions sitting in limits at infinity of the space. Following this heuristics, and building on top of results by Ritoré--Rosales and Nardulli, I will state a generalized existence result for the isoperimetric problem on Riemannian manifolds with Ricci curvature bounded from below and a uniform bound from below on the volumes of unit balls. The main novelty in such an approach is the use of the synthetic theory of curvature bounds to describe in a rather natural way where the mass is lost at infinity. Later, I will use the latter described generalized existence result to prove new existence criteria for the isoperimetric problem on manifolds with nonnegative Ricci curvature. In particular, I will show that on a complete manifold with nonnegative sectional curvature and Euclidean volume growth at infinity, isoperimetric regions exist for every sufficiently big volume. Time permitting, I will describe some forthcoming works and some open problems.

This talk is based on several papers and ongoing collaborations with E. Bruè, M. Fogagnolo, S. Nardulli, E. Pasqualetto, M. Pozzetta, and D. Semola. ]]>

Curtis homomorphisms in invariant theory

Tags: TAG Events DMI]]>

Positivity Preserving Limiters for Time-Implicit Higher Order Accurate Discontinuous Galerkin Discretizations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In this presentation, we will discuss a different approach to ensure that a higher order accurate DG solution satisfies the positivity constraints. Instead of using a limiter, we impose the positivity constraints directly on the algebraic equations resulting from a higher order accurate time-implicit DG discretization using techniques from mathematical optimization theory. This approach ensures that the positivity constraints are satisfied and does not affect the higher order accuracy of the time-implicit DG discretization. The resulting algebraic equations are then solved using a specially designed semi-smooth Newton method that is well suited to deal with the resulting nonlinear complementarity problem. We will demonstrate the algorithm on several parabolic model problems.

For further information about the seminar, please visit this webpage.

]]>18.11.2021 17:00 - 18.11.2021 18:00, Zoom: register here: https://www.ntwebseminar.org/

Towards uniformity in the dynamical Bogomolov

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Zahlentheorie]]>

In this talk we discuss uniform versions of the dynamical Bogomolov conjecture across 1-parameter families of certain split maps. To this end, we establish an instance of a 'relative dynamical Bogomolov'. This is work in progress joint with Harry Schmidt (University of Basel).

For further information about the seminar, please visit this webpage.

]]>Mod-φ approximation schemes: theory and applications to credit risk

Tags: TAG Events DMI]]>

Scales of Knowledge - Multilevel Minimization in Scientific Computing and Machine Learning

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Traditional multilevel decompositions are the basic ingredient of the most efficient class of solution methods for linear systems, i.e. of multigrid methods, which allow to solve certain classes of linear systems with optimal complexity. The transfer of these concepts to non-linear problems, however, is not straightforward, neither in terms of the design of the multilevel decomposition nor in terms of convergence properties. In this talk, we will discuss multilevel decompositions for convex, non-convex and possibly non-smooth minimization problems. We will discuss in detail how multilevel optimization methods can be constructed and analyzed and we will illustrate the sometimes significant gain in performance, which can be achieved by multilevel minimization techniques. Examples from mechanics, geophysics, and machine learning will illustrate our discussion.

For further information about the seminar, please visit this webpage.

]]>11.11.2021 17:00 - 11.11.2021 18:00, Zoom: register here: https://www.ntwebseminar.org/

Randomness

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Zahlentheorie]]>

Humanity has pondered the meaning and utility of randomness for millennia.

There is a remarkable variety of ways in which we utilize perfect coin tosses to our advantage: in statistics, cryptography, game theory, algorithms, gambling... Indeed, randomness seems indispensable! Which of these applications survive if the universe had no (accessible) randomness in it at all? Which of them survive if only poor quality randomness is available, e.g. that arises from somewhat "unpredictable" phenomena like the weather or the stock market?

A computational theory of randomness, developed in the past several decades, reveals (perhaps counter-intuitively) that very little is lost in such deterministic or weakly random worlds. In the talk I'll explain the main ideas and results of this theory, notions of pseudo-randomness, and connections to computational intractability.

It is interesting that Number Theory played an important role throughout this development. It supplied problems whose algorithmic solution make randomness seem powerful, problems for which randomness can be eliminated from such solutions, and problems where the power of randomness remains a major challenge for computational complexity theorists and mathematicians. I will use these problems (and others) to demonstrate aspects of this theory.

For further information about the seminar, please visit this webpage.

]]>Instabilities in vortex ring dynamics

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Real Forms on Complex Varieties

Tags: TAG Events DMI]]>

Machine Learning meets Numerical Simulation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We give examples of different types of combinations using exemplary approaches of simulation-assisted machine learning and machine-learning assisted simulation. We also discuss an advanced pairing where we see particular further potential for hybrid systems.

For further information about the seminar, please visit this webpage.

]]>Geometric Measure Theory: Regularity for the Plateau Problem

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Utility Maximization in a Market with an Arbitrage Opportunity

Tags: TAG Events DMI]]>

Öffentlicher Vortrag von Silvan Heller, Preisträger des Nachwuchsförderpreises der Studentenverbindung Schwizerhüsli

Tags: TAG Events Forschung Informatik, TAG Events DMI]]>

Im Anschluss an den Vortrag findet ein Apéro im Vereinslokal (Socinstrasse 8, 4051 Basel) statt.

**Voraussetzung für die Teilnahme am Event ist ein gültiges Covid-Zertifikat. Bitte beachten Sie, dass der Einlass aufgrund der Zertifikatskontrolle über die Hebelstrasse 12 erfolgt.**

Measure-Valued Solutions for the Compressible Euler Equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Error analysis for physics informed neural networks

Tags: TAG Events DMI]]>

Data-Driven Analytics for Decision Making in Game Sports

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Für den Zugangslink kontaktieren Sie bitte Prof. Heiko Schuldt (heiko.schuldt@unibas.ch).

]]>Boundary Element Methods for Shape Optimisation in Homogenisation

Tags: TAG Events DMI]]>

Analysis and Applications of Leapfrog-Based Local Time-Stepping Methods

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Für den Zugangslink kontaktieren Sie bitte Simon Michel (simon.michel@unibas.ch).

]]>Hier finden Sie das Programm zur Informationsveranstaltung für die Erstsemestrigen im Studium der Mathematik und der Informatik

Tags: TAG Events DMI, TAG Events Studium Informatik, TAG Events Studium Mathematik, TAG Events Forschung Informatik, TAG Events Forschung Mathematik]]>

Bei Fragen wenden Sie sich bitte an Heidi Karypidis (Mathematik) oder an Heike Freiberger (Informatik).

]]>Die Schweizerische Akademie der Naturwissenschaften (SCNAT) zeichnet mit dem Prix Schläfli junge Forschende an Schweizer Hochschulen aus.

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Die Teilnahme an der Preisverleihung ist registrierungspflichtig. Teilnehmende benötigen zudem ein gültiges Covid-Zertifikat.

Wenn Sie an der Preisverleihung teilnehmen möchten, melden Sie sich bitte hier an:

Wenn Sie am Apéro teilnehmen möchten, melden Sie sich bitte ** zusätzlich** hier an:

Die Teilnehmenden der Studienwoche Fascinating Informatics präsentieren ihre Ergebnisse.

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Rational points of small height on elliptic curves

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

The talk is open to members of the university.

For the access link, please contact Gaston Joachim Petit (joachim.petit@unibas.ch).

]]>Waves, learning, and inverse problems

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Boltzmann-Grad limit of a hard sphere system in a box with diffusive boundary conditions]]>

In its formal derivation Boltzmann supposed that two different particles are almost independent, so the probability of having two particles at the same place is the the product of probability. The validity of such equation is *a priori *not clear since it adds some irreversibly that does not exist in the hard sphere model.

Lanford solved the problem in its ‘75 paper: Boltzmann’s equation is true, up to a time independent of the number of particles (however each particle will have in mean less than one collision).

Now comes the question of the boundary. We expect to find some “Lanfords” theorem even if we add some boundary condition. A first example are the specular reflections, for a deterministic law. An other example, which would be very important in physics, is the evolution of a gas between two hot plaques. Then the reflection condition is stochastic. I am interested in a third type of reflection, also stochastic, which is a modeling of a rough boundary.

During my talk I will present some ideas of the proof of Boltzmann in the torus R^3/Z^3 and the adaptation in the case of a domain with boundaries.

]]>Der Verein «We are Computer Science» lädt zur Vorführung des Dokumentarfilms «Picture a Scientist» ein.

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Der Trailer ist hier verfügbar.

Die Dokumentation wird vom **28. Mai um 12:00 Uhr bis zum 30. Mai um 12:00 Uhr** über einen personalisierten Vimeo-Link verfügbar sein. Der Film kann in diesem Zeitraum jederzeit angesehen werden. Um auf den Link zuzugreifen, füllen Sie bitte**dieses Formular** aus.

**Da die Anzahl der Tickets begrenzt ist, werden diese bevorzugt an die Mitglieder des Vereins «We are Computer Science» vergeben, gefolgt von Studierenden und Mitgliedern des Departement Mathematik und Informatik an der Universität Basel. Alle übrigen Tickets werden frei an sonstige Interessenten vergeben.**

Generalizations of the half-wave maps equation]]>

Semiclassical limit for almost fermionic anyons]]>

Quasi-particles obeying such statistics can be described as ordinary bosons and fermions with magnetic interactions.

We study a limit situation where the statistics/magnetic interaction is seen as a “perturbation from the fermionic end”.

We vindicate a mean-field approximation, proving that the ground state of a gas of anyons is described to leading order by a semi-classical, Vlasov-like, energy functional.

The ground state of the latter displays anyonic behavior in its momentum distribution. After introducing and stating this result I will give elements of proof based on coherent states,

Husimi functions, the Diaconis-Freedman theorem and a quantitative version of a semi-classical Pauli pinciple.

]]>Ein Vortrag von Dr. Monica Landoni, Leiterin einer Forschungsgruppe an der Fakultät für Informatik der Università della Svizzera italiana.

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Ihre Forschungsgebiete liegen vor allem in der Interactive Information Retrieval und im Electronic Publishing, insbesondere im Gebiet Design und Evaluation von Kind-Computer Interaktion beim Lesen, Schreiben und Forschen. Sie ist sehr interessiert daran zu erforschen, wie Design für Gender Gleichgewicht, Zugänglichkeit und Inklusivität genutzt werden kann.

Die Veranstaltung ist öffentlich und kostenfrei über den Anmeldelink zugänglich.

]]>Benchpress: A scalable and platform independent workflow for benchmarking structure learning algorithms for graphical models

Tags: TAG Events DMI]]>

Counting sheaves and boxes

Tags: TAG Events DMI]]>

High order finite element methods for inverse initial value problems and wave propagation in heterogeneous media

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Splines in computer graphics and numerical methods

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>All Orders of the Dynamics of Bosons in the Mean-field Limit ]]>

This is joint work with Lea Bossmann, Peter Pickl, and Avy Soffer.

]]>Additive noise models for causal learning

Tags: TAG Events DMI]]>

Wavenumber-explicit hp-FEM analysis for the Helmholtz equation in heterogeneous media

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Joint work with: Maximilian Bernkopf (TU Wien), Théophile Chaumont-Frelet (Inria).

**References**

[EM11] S. Esterhazy and J.M. Melenk, On stability of discretizations of the Helmholtz equation, in: Numerical Analysis of Multiscale Problems, Graham et al., eds, Springer 2012

[MS10] J.M. Melenk and S. Sauter, Convergence Analysis for Finite Element Discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions, Math. Comp. 79:1871–1914, 2010

[MS11] J.M. Melenk and S. Sauter, Wavenumber explicit convergence analysis for finite element discretizations of the Helmholtz equation, SIAM J. Numer. Anal., 49:1210–1243, 2011

[MSP12] J.M. Melenk, S. Sauter, A. Parsania, Generalized DG-methods for highly indefinite Helmholtz problems, J. Sci. Comp. 57:536–581, 2013

For further information about the seminar, please visit this webpage.

]]>About some subgroups of the De Jonquières Group

Tags: TAG Events DMI]]>

A Nonlinear Spectral Analysis of Gradient Flows

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Vortrag von Prof. Florina Ciorba zum Thema "To study or not to study computer science"

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

On Arithmetic Dynamical Systems]]>

Nonlinear acoustics: time integration, optimization, and open domain problems

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

- absorbing boundary conditions for the treatment of open domain problems;
- optimization tasks for ultrasound focusing.

Strictly speaking, acoustic sound propagation takes place in full space or at least in a domain that is typically much larger than the region of interest Ω. To restrict attention to a bounded domain Ω, e.g, for computational purposes, artificial reflections on the boundary ∂Ω have to be avoided. This can be done by imposing so-called absorbing boundary conditions ABC that induce dissipation of outgoing waves. Here it will turn out to be crucial to take into account nonlinearity of the PDE also in these ABC. This is joint work with Igor Shevchenko (Imperial College London).

In the context of applications in HIFU, focusing of nonlinearly propagating waves amounts to optimization problems. The design of ultrasound excitation via piezoelectric transducers leads to a boundary control problem; focusing high intensity ultrasound by a silicone lens requires shape optimization. For both problem classes, we will discuss the derivation of gradient information in order to formulate optimality conditions and drive numerical optimization methods. This is joint work with Christian Clason (University of Duisburg-Essen), Vanja Nikolić (TU München), and Gunther Peichl (University of Graz).

Finally we will provide an outlook on imaging with nonlinearly acoustic waves, which amounts to identifying spatially varying coefficients (sound speed and/or coefficient of nonlinearity) in the Westervelt equation. This is recent joint work with Masahiro Yamamoto (University of Tokyo) and William Rundell (Texas A&M University).

For further information about the seminar, please visit this webpage.

]]>Almost everywhere non-uniqueness for integral curves of Sobolev vector fields

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Online-Vortrag im Rahmen der Ringvorlesung «Künstliche Intelligenz im Recht»

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

**Eröffnung der Ringvorlesung:**Prof. Dr. Wolfgang Wohlers, Dekan der Juristischen Fakultät, und Prof. Dr. Bijan Fateh-Moghadam, Leiter des Doktoratsprogramms «Recht im Wandel»**Können wir Künstlicher Intelligenz vertrauen?**Prof. Dr. Malte Helmert, Professor für Informatik, Universität Basel**Intelligente Maschinen als moralische Akteure:**Lukas Brand, Doktorand am Lehrstuhl für Religionsphilosophie und Wissenschaftstheorie, Bochum

Moderation: Prof. Dr. Bijan Fateh-Moghadam, Universität Basel

Die Vorlesungsreihe wird digital durchgeführt. Für die Teilnahme an der öffentlichen Ringvorlesung ist eine Registrierung erforderlich. Danach erhalten Sie eine Bestätigungs-E-Mail mit Informationen zur Teilnahme am Webinar.

**Veranstalter:**

Juristische Fakultät

Inviscid mixing with fluid flows - Optimal stirring with cellular and radial velocity fields

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Für den Zugangslink kontaktieren Sie bitte Prof. Gianluca Crippa (gianluca.crippa@unibas.ch).

]]>

Implementation of a pathfollowing strategy with an automatic step-length control in the new MATLAB package bvpsuite2.0

Tags: TAG Events DMI]]>

The trajectories of the Schrödinger equation]]>

This is related to the control problem, i.e. driving the system to a target state, which turns out to be impossible for "typical" target states using bounded potentials. ]]>

Der Infoabend zum Masterstudium an der Universität Basel findet am 18. März 2021 digital statt.

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik, TAG Events Studium Actuarial Science]]>

**17:00-17:45** Präsentation**18:00-18:45** Offene Sprechstunde**19:00-19:45** Offene Sprechstunde

Zugangslink: https://unibas.zoom.us/j/95298357874?pwd=V1o1RzlLdFd2a0oxLzBEY1piSmhJUT09

**17:00-18:00** Offene Sprechstunde**18:00-18:45** Präsentation**18:45-20:00** Offene Sprechstunde

Zugangslink: https://unibas.zoom.us/j/98957600025?pwd=V05LZjlUb1VJQ1NMRSt6aXV0N2VYUT09

**17:00-17:45** Präsentation, anschliessend offene Sprechstunde (I)**18:00-18:45** Meet our Students**19:00-19:45** Präsentation, anschliessend offene Sprechstunde (II)

Zugangslink Sprechstunden I und II: https://unibas.zoom.us/j/98135667870

Zugangslink Meet our Students: https://unibas.zoom.us/j/94100921756

Weitere Informationen finden Sie auf der Webseite des Basler Infoabend Master.

]]>Bosons in a double well: two-mode approximation and fluctuations]]>

The leading-order physics is governed by a Bose-Hubbard Hamiltonian coupling two low-energy modes, each supported in the bottom of one well. Fluctuations beyond these two modes are ruled by two independent Bogoliubov Hamiltonians, one for each well.

Our main result is that the variance of the number of particles in the low-energy modes is suppressed. This is a violation of the Central Limit Theorem which holds in the occurrence of Bose-Einstein condensation, and therefore it signals that particles develop correlations in the ground state. We achieve our result by proving a precise energy expansion in term of Bose-Hubbard and Bogoliubov energies.

Joint work with Nicolas Rougerie (ENS Lyon) and Dominique Spehner (Universidad de Concepción). ]]>

Classification of quartic plane Cremona maps with a maximum of two proper base points

Tags: TAG Events DMI]]>

Multilevel Scheduling of Computations on Parallel Large-scale Systems

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Understanding the relation between different scheduling levels is crucial for solving the aforementioned research question. However, it is challenging due to (1) the absence of methods, models, and tools to examine and analyze the interaction and the mutual impact of these scheduling levels, and (2) the different nature and performance targets of each of these scheduling levels. This doctoral dissertation addresses these challenges in the context of two specific HPC scheduling classes: queuing-based job scheduling at the batch level and dynamic loop self-scheduling (DLS) at the application level. One of the main contributions of this doctoral dissertation is proposing and evaluating a multilevel scheduling (MLS) prototype that effectively solves the problem by bridging the schedulers at different scheduling levels. The MLS prototype aims to (1) decrease applications’ execution time and (2) increase system utilization. The MLS prototype employs two novel scheduling approaches introduced in this doctoral dissertation. The first approach is the distributed chunk calculation approach (DCA) and its hierarchical version (HDCA). The second approach is the resourceful coordination approach (RCA).

At the application level, the DCA and HDCA address the scalability challenge of existing DLS implementations. We apply DCA and HDCA to several state-of-the-art DLS techniques, and show how they benefit applications’ execution time; therefore, fulfilling the MLS prototype’s first target. At the batch level, the RCA enables application schedulers to share their allocated but idle computing resources with other applications through a batch system. The significance of RCA is that it leverages and combines the advantages of node sharing and dynamic resource management. It offers efficient resource sharing and avoids shrinkage and expansion operations at the application side. RCA allows batch systems to reassign computing resources once they become free; therefore, fulfilling the MLS prototype’s second target. By employing DCA and RCA, the MLS prototype answers the aforementioned research question and shows a creative and useful way for exploiting the multilevel parallelism of modern HPC systems through scheduling.

This doctoral dissertation advances the state-of-the-art by demonstrating the usefulness and the performance potential of coordinated scheduling decisions at different levels. Moreover, this doctoral dissertation introduces certain methods and tools that allow the HPC community to analyze the mutual impact of scheduling decisions at different scheduling levels.

**Der Vortrag ist universitätsöffentlich.**

**Für den Zugangslink kontaktieren Sie bitte Prof. Florina Ciorba (florina.ciorba@unibas.ch).**

Derivation of the Vlasov equation: Different types of convergence]]>

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik]]>

- offene Sprechstunde Mathematik
- offene Sprechstunde Informatik
- Fachgruppe Mathematik und Informatik kennenlernen
- We Are Computer Science Association kennenlernen
- Forschungsgruppen und Schwerpunkte entdecken

Schülerinnen und Schüler, die sich für die Bachelorstudiengänge Mathematik und/oder Informatik interessieren, sind herzlich eingeladen teilzunehmen.

]]>Tags: TAG Events DMI, TAG Events Studium Mathematik, TAG Events Studium Informatik, TAG Events Forschung Informatik, TAG Events Forschung Mathematik]]>

Weitere Informationen sowie Links zu den einzelnen Veranstaltungen finden Sie **hier**.

Optimal regularity for viscous Hamilton-Jacobi equations in Lebesgue spaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Modelling Auctions: Winning Bets, Betting on Wins]]>

High-order finite element methods for the fractional Laplacian

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

]]>Alle Mitglieder des Departements, insbesondere Studierende aller Fachsemester, sind herzlich eingeladen

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik]]>

Leslie Lamport erhielt 2013 den Turing Award "for fundamental contributions to the theory and practice of distributed and concurrent systems, notably the invention of concepts such as causality and logical clocks, safety and liveness, replicated state machines, and sequential consistency". Neben diesen wissenschaftlichen Kernbeiträgen ist er auch für die Erfindung des LaTeX-Dokumentationsvorbereitungssystems bekannt.

In der Fragerunde liegt der Fokus auf Lamports technischen Beiträgen und deren Auswirkungen, seinen Ansichten zur Vergangenheit, Gegenwart und Zukunft der Informatik sowie seinen Gedanken zum wissenschaftlichen Schreiben und zum Leben als Forscher fragen. Die Sitzung wird moderiert und basiert hauptsächlich auf Fragen der Seminarteilnehmenden. Am Ende besteht die Möglichkeit Fragen zu stellen.

]]>High-regularity Invariant Measures for 2d and 3d Euler Equations and Growth of the Sobolev Norms

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

In this talk, I will present some results obtained in this direction. We will construct invariant measures for the 2d Euler equation at high regularity ($H^s$, $s>2$) and prove that on the support of the measure, Sobolev norms do not grow faster than polynomially.

Refining the method allows to construct an invariant measure to the 3d Euler equations at high regularity ($H^s$, $s>7/2$) and thus construct

global dynamics on the support of the measure, exhibiting at most polynomial growth.

Finally, it time permits we will discuss the properties of the measures constructed. ]]>

Asymptotic expansion of low-energy excitations for weakly interacting bosons

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

We consider a system of N bosons in the mean-field scaling regime in an external trapping potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N. We show that the structure of the ground state and of the non-degenerate low-energy eigenstates is preserved by the dynamics if

the external trap is switched off. This talk is based on joint works with Sören Petrat, Peter Pickl, Robert Seiringer, and Avy Soffer (arXiv:1912.11004 and arXiv:2006.09825).

Musical mathematics ]]>

Uniqueness and global convergence for a discretized inverse coefficient problem

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We then demonstrate that this result can be used to prove uniqueness, stability and global convergence for an inverse coefficient problem with finitely many measurements. We consider the problem of determining an unknown inverse Robin transmission coefficient in an elliptic PDE. Using a relation to monotonicity and localized potentials techniques, we show that a piecewise-constant coefficient on an a-priori known partition with a-priori known bounds is uniquely determined by finitely many boundary measurements and that it can be uniquely and stably reconstructed by a globally convergent Newton iteration. We derive a constructive method to identify these boundary measurements, calculate the stability constant and give a numerical example.

For further information about the seminar, please visit this webpage.

Radial symmetry in stationary/uniformly-rotating solutions to 2D Euler equation

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Convex Integration in a Nutshell

Tags: TAG Events Forschung Mathematik, TAG Events Perlenkolloquium, TAG Events DMI]]>

The dilute Fermi gas via Bogoliubov theory

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

We consider N spin 1/2 fermions interacting with a positive

and regular enough potential in three dimensions. We compute the ground

state energy of the system in the dilute regime at second order in the

particle density. We recover a well-know expression for the ground state

energy which depends on the interaction potentials only via its

scattering length. A first proof of this result has been given by Lieb,

Seiringer and Solovej. We discuss a new derivation of this formula

which makes use of the almost-bosonic nature of the low-energy

excitations of the systems. Based on a joint work with Marco Falconi,

Christian Hainzl, Marcello Porta. ]]>

Feller Dynamics of Exchangeable Arrays]]>

Adaptive time-stepping for S(P)DEs with non-Lipschitz drift

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

A birational journey: From plane curve singularities to the Cremona group over perfect fields]]>

Runge-Kutta based local time-stepping methods for forced wave equations]]>

Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with oblique boundary conditions

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

This is joint work with Guillaume Bertoli (Université de Genève) and Christophe Besse (Institut de Mathématiques de Toulouse).

For further information about the seminar, please visit this webpage.

]]>Existence of weak solutions and incompressible limit for quantum Navier-Stokes equations

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

First, we prove global existence of finite energy weak solutions (FEWS) in dimension two and three. To compensate for the lack of control of the velocity field around vacuum regions, we construct approximate solutions to a truncated formulation of (QNS) on a sequence of invading domains. Suitable compactness properties are inferred from the Bresch-Desjadins entropy estimates. This is joint work with P. Antonelli and S. Spirito.

Second, we address the low Mach number limit for FEWS to the (QNS) system (in collaboration with P. Antonelli and P. Marcati). The main novelty is a precise analysis of the acoustic dispersion altered by the presence of the dispersive capillarity tensor. The linearised system is governed by the Bogoliubov dispersion relation. The desired decay of the acoustic part follows from refined Strichartz estimates.

]]>Modular method for solving Diophantine equations]]>

Variational Problems in Quasi-Classical Systems

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

In this talk I will overview variational problems arising from the study ofquantum matter interacting with a macroscopic force field. These interactions are verycommon in both solid state and condensed matter physics, as well as in higher energysettings. In particular, I will focus on the link between the effective and microscopicdescription of such variational problems, using techniques of quasi-classical analysisdeveloped in recent years in collaboration with M. Correggi and M. Olivieri.

]]>The Liouville equation, its extensions, and related optimal control problems

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

This talk provides an introduction to the formulation and solution of optimal control problems governed by the Liouville equation and related models. The purpose of this framework is the design of robust controls to steer the motion of particles, pedestrians, etc., where these agents are represented in terms of density functions. For this purpose, expected-value cost functionals are considered that include attracting potentials and different costs of the controls, whereas the control mechanism in the governing models is part of the drift or is included in a collision term.

In this talk, theoretical and numerical results concerning ensemble optimal control problems with Liouville, Fokker-Planck and linear Boltzmann equations are presented.

For further information about the seminar, please visit this webpage.

A posteriori Error Estimates for Numerical Solutions to Hyperbolic Conservation Laws

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

An evolutionary, fast, and oblivious compression approach to Volterra integral operators

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this webpage.

Are weak solutions to the supercritical surface quasigeostrophic equation smooth a.e.?

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

On the stability of a point charge for the Vlasov-Poisson system

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Fourier interpolation problems and modular forms]]>

Variational problems for nonlinear Schroedinger equations on metric graphs

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Iterative Methods for Linear Systems over two Centuries

Tags: TAG Events Perlenkolloquium, TAG Events Forschung Mathematik]]>

Iterative methods for linear systems were invented for the same reasons as they are used today, namely to reduce computational cost. Gauss states in a letter to his friend Gerling in 1823: "you will in the future hardly eliminate directly, at least not when you have more than two unknowns". Richardson's paper from 1910 was then very influential, and is a model of a modern numerical analysis paper: modeling, discretization, approximate solution of the discrete problem, and a real application. More general vector extrapolation methods were then introduced and studied in the pioneering work of Bresinzki, and they can be shown to be equivalent to Krylov method. It was however the work of Stiefel, Hestenes and Lanczos in the early 1950 that sparked the success story of Krylov methods with the invention of the conjugate gradient method, and there are now many Krylov methods to choose from. For general linear systems, they come in two main classes, the ones that minimize the residual in a Krylov space, and the ones that make the residual orthogonal to it. This will bring us finally to the modern iterative methods for solving partial differential equations, which also come in two main classes: domain decomposition methods and multigrid methods. Domain decomposition methods go back to the alternating Schwarz method invented by Herman Amandus Schwarz in 1869 to close a gap in the proof of Riemann's famous Mapping Theorem. Multigrid goes back to the seminal work by Fedorenko in 1961, with main contributions by Brandt and Hackbusch in the Seventies.

]]>Sharp energy regularity and typical wild solutions of the incompressible Euler equations

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Actions of Cremona groups on CAT(0) cube complexes.

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

In this talk, based on a common work with Christian Urech, we will construct such complexes on which Cremona groups of rank n act. We will then see which kind of results on these groups we can obtain.

]]>Protocol Replicating Social Graphs - Scuttlebutt

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

Please register via **christian.tschudin@unibas.ch**.

Computer-based formal proof in computer science and mathematics

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

]]>

Öffentliche Veranstaltung

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Begrüssung:

Gianluca Crippa, Departementsvorsteher

A.M. Ostrowski und die Präsentation des Preises:

Helmut Harbrecht, Präsident der Ostrowski-Stiftung

Laudatio:

Terence Tao, University of California, Los Angeles

Überreichung der Medaille der Ostrowski-Stiftung

Preisvortrag durch den Preisträger Assaf Naor

Im Anschluss an die Zeremonie wird ein Apéro offeriert.

]]>81 Jahre Versicherungsmathematik an der Universität Basel

Tags: TAG Events DMI]]>

Am 6. Februar 1939 wurde Versicherungslehre an der Universität Basel als selbständiges Examensfach eingeführt. Anlässlich des 80jährigen Bestehens wurde im Februar 2019 AlumniActuarialScience gegründet.

In Zusammenarbeit mit dem Masterstudiengang organisiert AlumniActuarialScience exakt ein Jahr später eine 2. Reunion. Drei Actuarial Science-Studentinnen stellen ihre Abschlussarbeiten vor und Prof.em.Dr. Herbert Lüthy gibt einen kurzen Überblick zur Entwicklung der Versicherungsmathematik. Beim anschliessenden Apéro bietet sich Gelegenheit, Studienkolleg*innen und Dozent*innen wiederzusehen sowie andere Aktuar*innen aus der Region kennenzulernen.

Alle Interessierten sind herzlich eingeladen.

**Anmeldung**

Für die Vorträge und den anschliessenden Apéro in der Alten Universität ist keine Anmeldung erforderlich.

Das AlumniEssen findet im Restaurant *Zum Isaak* statt und ist für Mitglieder *AlumniActuarialScience* und solche, die es gerne werden wollen. Bitte anmelden bis am 26. Januar 2020 an info@*clutter*AlumniActuarialScience.ch.

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Weitere Informationen: AlumniActuarialScience.

]]>Münsterschatz im Virtuellen Museum

Tags: TAG Events DMI]]>

am Donnerstag, den 9. Januar 2020 ab 09:00 Uhr

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Numerical methods for fractional PDEs with applications to spatial statistics

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We propose an approximation supported by a rigorous error analysis which shows different notions of convergence at explicit and sharp rates. We furthermore discuss the computational complexity of the proposed method. Finally, we present several numerical experiments, which attest the theoretical outcomes, as well as a statistical application where we use the method for inference, i.e., for parameter estimation given data, and for spatial prediction.

For further information about the seminar, please visit this webpage.

]]>Fontes-Isopi-Newman processes associated with resistance forms]]>

Optimal errors and phase transitions in high-dimensional generalised linear models]]>

High-dimensional generalized linear models are basic building blocks of current data analysis tools including multilayers neural networks. They arise in signal processing, statistical inference, machine learning, communication theory, and other fields. I will explain how to establish rigorously the intrinsic information-theoretic limitations of inference and learning for a class of randomly generated instances of generalized linear models, thus closing several old conjectures. Examples will be shown where one can delimit regions of parameters for which the optimal error rates are efficiently achievable with currently known algorithms. I will discuss how the proof technique, based on the recently developed adaptive interpolation method, is able to deal with the output nonlinearity and also to some extent with non-separable input distributions. |

Fluctuation of the free energy of Sherrington-Kirkpatrick model with Curie-Weiss interaction: the paramagnetic regime]]>

We consider a spin system containing pure two spin Sherrington-Kirkpatrick Hamiltonian with Curie-Weiss interaction. The model where the spins are spherically symmetric was considered by Baik and Lee and Baik et al. which shows a two dimensional phase transition with respect to temperature and the coupling constant. In this paper we prove a result analogous to Baik and Lee in the “paramagnetic regime” when the spins are i.i.d. Rademacher. We prove the free energy in this case is asymptotically Gaussian and can be approximated by a suitable linear spectral statistics. Unlike the spherical symmetric case the free energy here can not be written as a function of the eigenvalues of the corresponding interaction matrix. The method in this paper relies on a dense sub-graph conditioning technique introduced by Banerjee . The proof of the approximation by the linear spectral statistics part is close to Banerjee and Ma. | |

High order finite element discretizations of Helmholtz problems

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

It has received much attention since it is widely employed in applications,

but still challenging to numerically simulate in the high-frequency regime.

In this seminar, we focus on acoustic waves for the sake of simplicity

and consider finite element discretizations. The main goal of the

presentation is to highlight the improved performance of high order

methods (as compared to linear finite elements) when the frequency is large.

We will very briefly cover the zero-frequency case, that corresponds to the well-studied Poisson equation. We take advantage of this classical setting to recall central concepts of the finite element theory such as quasi-optimality and interpolation error.

The second part of the seminar is devoted to the high-frequency case.

We show that without restrictive assumptions on the mesh size,

the finite element method is unstable, and quasi-optimality is lost.

We provide a detailed analysis, as well as numerical examples, which

show that higher order methods are less affected by this phenomena,

and thus more suited to discretize high-frequency problems.

Before drawing our main conclusions, we briefly discuss advanced topics,

such as the use of unfitted meshes in highly heterogeneous media

and mesh refinements around re-entrant corners.

For further information about the seminar, please visit this webpage.

]]>zum Thema Random Diophantine Equations

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Perlenkolloquium]]>

Zero-one laws for first order properties of random graphs]]>

Zero-one laws for first order properties of random graphs]]>

Direct/Inverse Hopfield model and Restricted Boltzmann Machines]]>

Mean-field methods fail to reconstruct the parameters of the model when the dataset is clusterized. This situation is found at low temperatures because of the emergence of multiple thermodynamic states. The paradigmatic Hopfield model is considered in a teacher-student scenario as a problem of unsupervised learning with Restricted Boltzmann Machines (RBM). For different choices of the priors on units and weights, the replica symmetric phase diagram of random RBM’s is analyzed and in particular the paramagnetic phase boundary is presented as directly related to the optimal size of the training set necessary for a good generalization. The connection between the direct and inverse problem is pointed out by showing that inference can be efficiently performed by suitably adapting both standard learning techniques and standard approaches to the direct problem. | |

]]>

Prelog Chow rings and stable rationality in semistable degenerations

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

On error estimates for optimal control problems with functions of bounded variation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We consider a convex optimal control problem governed by a partial differential equation in one space dimension which is controlled by a right-hand-side living in the space of functions with bounded variation. These functions tend to favor optimal controls that are piecewise constant with often finitely many jump poins. We are interested in deriving finite element discretization error estimates for the controls when the state ist discretized with usual piecewise linear finite elements, and the controls is either variationally discrete or piecwise constant. Due to the structure of the objective function, usual techniques for estimating the control error cannot be applied. Instead, these have to be derived from (suboptimal) error estimates for the state, which can later be improved.

For further information about the seminar, please visit this webpage.

]]>Classification of simple singularities]]>

Birational models of terminal sextic double solids

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Automorphisms of Del Pezzo surfaces of degree 4]]>

Maximum Likelihood Estimation of Toric Fano Varieties

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Unlikely Intersections with Isogeny Orbits

Tags: TAG Events DMI, TAG Events Perlenkolloquium, TAG Events Forschung Mathematik]]>

Leonhard Euler's methods of celestial mechanics (Beginn: 15:15 Uhr)

Tags: TAG Events Forschung Mathematik, TAG Events Forschung Informatik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Details zum Anlass finden sich auf der Webseite des Departements Physik.

]]>Anisotropic vector fields: quantitative estimates and applications to the Vlasov-Poisson equation

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Perlenkolloquium]]>

The Cauchy problem for the quantum hydrodynamics system and the stability of weak solutions

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Oscillatory behaviour in coagulation-fragmentation models

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Numerical aspects of elliptic diffusion problems on random domains

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

For further information about the seminar, please visit this webpage.

]]>Algebraic torus actions

Tags: TAG Events DMI, TAG Events Perlenkolloquium, TAG Events Forschung Mathematik]]>

Lower bounds of non-vanishing sums (part 2) ]]>

Dual complexes of degenerations and Berkovich geometry

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

]]>

Aposteriori error analysis and adaptive schemes for the wave equation

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Notes: This is based on joint work with E.H. Georgoulis, C. Makridakis and J.M. Virtanen.

References:

[1] W. Bangerth and R. Rannacher, J. Comput. Acoust. 9(2):575–591, 2001.

[2] C. Bernardi and E. Süli, Math. Models Methods Appl. Sci. 15(2):199--225, 2005.

[3] E. H. Georgoulis, O. Lakkis, and C. Makridakis. IMA J. Numer. Anal., 33(4):1245–1264, 2013, http://arxiv.org/abs/1003.3641

[4] E. H. Georgoulis, O. Lakkis, C. Makridakis, and J. M. Virtanen. SIAM J. Numer. Anal., 54(1), 2016, http://arxiv.org/abs/1411.7572

For further information about the seminar, please visit this webpage.

]]>Complex projective structures on Riemann surfaces]]>

Invitation to random tensors]]>

Birational Kleinian groups and birational structures

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Multirate explicit stabilized integrators for stiff differential equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The efficiency of these methods deteriorates as the system becomes stiffer, even if stiffness is induced by only few degrees of freedom. In the framework of discretized parabolic PDEs, the number of function evaluations has to be chosen inversely proportional to the smallest element size in order to achieve stability, thus largely wasting computational resources on locally-refined meshes. We first tackle this issue by replacing the right hand side of the PDE with an averaged force, which is obtained by damping the high modes down using the dissipative effect of the equation itself and which is cheap to evaluate. Combining RKC methods with the averaged force we give rise to multirate RKC schemes, for which the number of expensive function evaluations is independent of the small elements' size.

The stability properties of our method are demonstrated on a model problem and numerical experiments confirm that the stability bottleneck caused by a few of fine mesh elements can be overcome without sacrificing accuracy.

For further information about the seminar, please visit this webpage.

]]>On the frequency of height values]]>

On bulk deviations for the local behavior of random interlacements]]>

In this talk we will discuss some recent large deviation asymptotics concerning the local behavior of random interlacements on Z^d, d≥3. In particular, we will describe the link with previous results concerning macroscopic holes left inside a large box, by the the adequately thickened connected component of the boundary of the box in the vacant sets of random interlacements. | |

29.10.2019 18:15 - 29.10.2019 19:00, Fachgruppe Mathematik und Informatik, DMI, Spiegelgasse 1, Seminarraum 00.003

Christian Graf, Non-life pricing for commercial lines at Allianz Suisse

Tags: TAG Events DMI]]>

**Next event:**

November 12, 2019

Orhan Yildirim, Data Scientist at IWB (Deutsch)

]]>

Graded Rings and Birational Geometry

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

The main purpose of the talk is to give a short introduction to the theory and describe some of its applications.

]]>Lower bounds of non-vanishing sums]]>

C^0-closedness of the set of symplectomorphisms, spherical symplectic nonsqueezing, and holomorphic maps

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Symplectic geometry originated from classical mechanics, where the canonical symplectic form on phase space appears in Hamilton's equation. A (smooth) diffeomorphism on a symplectic manifold is called a symplectomorphism iff it preserves the symplectic form. This happens iff the diffeomorphism solves a certain inhomogeneous quadratic first order system of PDE's. In classical mechanics symplectomorphisms play the role of canonical transformations.

A famous result by Eliashberg and Gromov states that the set of symplectomorphisms is $C^0$-closed in the set of all diffeomorphisms. This is remarkable, since in general, the $C^0$-limit of a sequence of solutions of a first order system of PDE's need not solve the system. A well-known proof of the Eliashberg-Gromov theorem is based on Gromov's symplectic nonsqueezing theorem for balls.

In my talk I will sketch this proof. Furthermore, I will present a symplectic nonsqueezing result for spheres that sharpens Gromov's theorem. The proof of this result is based on the existence of a holomorphic map from the (real) two-dimensional unit disk to a certain symplectic manifold, satisfying some Lagrangian boundary condition. Such a map solves the Cauchy-Riemann equation for a certain almost complex structure. ]]>

22.10.2019 18:15 - 22.10.2019 19:00, Fachgruppe Mathematik und Informatik, DMI, Spiegelgasse 1, Seminarraum 00.003

Laurent Huber, Quantitative Insurance Specialist at Schroders, Investment Management

Tags: TAG Events DMI]]>

**Next events:**

October 29, 2019

Christian Graf, Non-life pricing for commercial lines at Allianz Suisse (English)

-------

November 12, 2019

Orhan Yildirim, Data Scientist at IWB (Deutsch)

]]>

tba

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Perlenkolloquium]]>

Two Puzzles in Particle Physics]]>

ℚ-homology planes satisfying the Negativity Conjecture

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Blowing up and automorphisms on a blow-up]]>

On continuous automorphisms of Cremona groups

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Pricescapes - Competitive Pricing Landscapes]]>

Mathematical modelling of transmission dynamics of Opisthorchis viverrini

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Perlenkolloquium]]>

Latest news about forthcoming Work Programme; Experiences and tips from successful applicants

Tags: TAG Events Forschung Informatik, TAG Events Forschung Mathematik, TAG Events Perlenkolloquium, TAG Events DMI]]>

In addition, information is provided how to identify topics of interest and find partners to submit proposals from basic research to market application.

Horizon 2020 project winners from academia and industry will give insights into running projects.

For the 2020 Work Programme, the areas of Artificial Intelligence (AI), digitizing European Industry, HPC, Big Data, Cloud technologies, 5G, Next Generation Internet (NGI) and key technologies for digital transformation from photonics to software, advanced and smart connectivity are prioritized.

Please register online.

]]>04.09.2019 08:30 - 06.09.2019 16:00

Summer School of the PhD Program Data Analytics

Tags: TAG Events DMI]]>

More information on the summer school and a link for the enrollment can be found here.

]]>02.09.2019 08:00 - 12.09.2019 17:00, Alte Universität, Rheinsprung 9

One week of mini-courses and a week-long conference held from September 2 till 13, 2019

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Zahlentheorie]]>

Website: numbertheory.dmi.unibas.ch/trip2019

]]>

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Finite subgroups of tame polynomial automorphisms

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Symmetry of Ground States by Fourier Rearrangement

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Tensor B-Spline Numerical Method for PDEs: a High Performance Approach

Tags: TAG Events DMI, TAG Events Forschung Informatik]]>

ABSTRACT:

Solutions of Partial Differential Equations (PDEs) form the basis of many mathematical models

in physics and medicine. In this work, a novel Tensor B-spline methodology for numerical

solutions of linear second-order PDEs is proposed. The methodology applies the B-spline

signal processing framework and computational tensor algebra in order to construct high-

performance numerical solvers for PDEs. The method allows high-order approximations, is

mesh-free, matrix-free and computationally and memory efficient.

The first chapter introduces the main ideas of the Tensor B-spline method, depicts the main

contributions of the thesis and outlines the thesis structure.

The second chapter provides an introduction to PDEs, reviews the numerical methods for

solving PDEs, introduces splines and signal processing techniques with B-splines, and describes

tensors and the computational tensor algebra.

The third chapter describes the principles of the Tensor B-spline methodology. The main

aspects are 1) discretization of the PDE variational formulation via B-spline representation

of the solution, the coefficients, and the source term, 2) introduction to the tensor B-spline

kernels, 3) application of tensors and computational tensor algebra to the discretized variational

formulation of the PDE, 4) tensor-based analysis of the problem structure, 5) derivation of

the efficient computational techniques, and 6) efficient boundary processing and numerical

integration procedures.

The fourth chapter describes 1) different computational strategies of the Tensor B-spline

solver and an evaluation of their performance, 2) the application of the method to the forward

problem of the Optical Diffusion Tomography and an extensive comparison with the state-

of-the-art Finite Element Method on synthetic and real medical data, 3) high-performance

multicore CPU- and GPU-based implementations, and 4) the solution of large-scale problems

on hardware with limited memory resources.

Der Vortrag ist universitätsöffentlich.

]]>

Gaussian fluctuations in directed polymers]]>

Recent results on singular limits for Vlasov-Poisson

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The Vlasov-Poisson system is a kinetic equation that models collisionless plasma. A plasma has a characteristic scale called the Debye length, which is typically much shorter than the scale of observation. In this case the plasma is called ‘quasineutral’. This motivates studying the limit in which the ratio between the Debye length and the observation scale tends to zero. Under this scaling, the formal limit of the Vlasov-Poisson system is the Kinetic Isothermal Euler system.

The Vlasov-Poisson system itself can formally be derived as the limit of a system of ODEs describing the dynamics of a system of N interacting particles, as the number of particles approaches infinity. The rigorous justification of this mean field limit remains a fundamental open problem.

In this talk we present how the mean field and quasineutral limits can be combined to derive the Kinetic Isothermal Euler system from a regularised particle model.

Quantitative seismic imaging using reciprocity waveform inversion with arbitrary probing sources

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We investigate the deployment of new devices developed in the acoustic setting: the dual-sensors, which are able to capture both the pressure field and the vertical velocity of the waves. For solving the inverse problem, we define a new cost function, adapted to these two types of data and based upon the reciprocity. We first note that the stability of the problem can be shown to be Lipschitz, assuming piecewise linear parameters. In addition, reciprocity waveform inversion allows a separation between the observational and numerical acquisitions. In fact, the numerical sources do not have to coincide with the observational ones, offering new possibilities to create adapted computational acquisitions, consequently reducing the numerical cost. We illustrate our approach with three-dimensional medium reconstructions, where we start with minimal information on the target models. We also extend the methodology for elasticity.

Eventually, if time allows, we shall explore the model representation in numerical seismic inversion, where the adaptive eigenspace method appears as a promising approach to have a compromise between number of unknowns and resolution.

References

[1] G. Alessandrini, M. V. de Hoop, F. Faucher, R. Gaburro and E. Sincich, Inverse problem for the Helmholtz equation with Cauchy data: reconstruction with conditional well-posedness driven iterative regularization, ESAIM: M2AN (2019).

[2] E. Beretta, M. V. De Hoop, F. Faucher, and O. Scherzer, Inverse boundary value problem for the Helmholtz equation: quantitative conditional Lipschitz stability estimates. SIAM Journal on Mathematical Analysis, 48(6), pp.3962-3983 (2016).

[3] M. J. Grote, M. Kray, and U. Nahum, Adaptive eigenspace method for inverse scattering problems in the frequency domain. Inverse Problems, 33(2), 025006 (2017).

[4] H. Barucq, F. Faucher, and O. Scherzer, Eigenvector Model Descriptors for Solving an Inverse Problem of Helmholtz Equation. arXiv preprint arXiv:1903.08991 (2019).

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage.

AlumniComputerScience

Tags: TAG Events Alumni Informatik, TAG Events DMI, TAG Events Forschung Informatik]]>

The talk will present some of the successful projects at Apple where Computer Vision and Machine Learning was used. It will include a deeper dive into the technology behind the real time facial motion capture on iPhone.

Dr. Brian Amberg studied „Information Science Cognition“ in Freiburg i. Brsg. From 2005 until 2010, he was a PhD in the research group of Prof. Dr. Vetter. In 2012, Amberg co-founded at EPFL

The Kuzenetsov Lemma for Conservation Laws with Space and Time Dependent Flux]]>

Thresholds for Measuring Degree in fractional Sobolev Spaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The degree of a map between two spheres of same dimension can be estimated by Sobolev norm of said map (of the right class). In this talk I will discuss to what extend this is possible for the Hopf degree as well – and why the estimate we have is “analytically optimal” but probably not “topologically optimal”. Joint work with J. Van Schaftingen.

]]>21.05.2019 14:00, Seminarraum 05.002, Spiegelgasse 5, Departement Mathematik und Informatik

Tags: TAG Events DMI, TAG Events Studium Informatik]]>

]]>

Mathematical Models of Cancer Evolution

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Adaptive Iterative Linearization Galerkin Methods for Nonlinear Partial Differential Equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage. ]]>

A Brief Look at Genomic Testing in Terms of Algebraic Statistics]]>

Random walk on a simple exclusion process]]>

In this talk we will study the asymptotic behavior of a random walk that evolves on top of a simple symmetric exclusion process. This nice example of a random walk on a dynamical random environment presents its own challenges due to the slow mixing properties of the underlying medium. We will discuss a law of large numbers that has been proved recently for this random walk. Interestingly, we can only prove this law of large numbers for all but two exceptional densities of the exclusion process. The main technique that we have employed is a multi-scale renormalization that has been derived from works in percolation theory. | |

14.05.2019 18:15, Seminarraum 00.003, Spiegelgasse 1, Departement Mathematik und Informatik

Stephan Heule, SBB, Data Scientist

Tags: TAG Events DMI, TAG Events Studium Informatik]]>

Wie sieht Deine berufliche Zukunft aus? Diese Vortragsreihe zeigt Dir spannende Karrierewege.

Der Vortrag findet um 18.15 Uhr im Seminarraum 00.003 in der Spiegelgasse 1 (Departement Mathematik und Informatik) statt.

]]>

14.05.2019 12:15 - 14.05.2019 13:15, DMI, Spiegelgasse 5, Basel, Raum 05.002

Heuristic Search: Something Old and Something New

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Alumni Informatik]]>

I begin this talk with a review of long-established results in heuristic search and the early history of bidirectional heuristic search. I then describe a recent (2016) breakthrough in bidirectional heuristic search (the MM algorithm), which challenges long-held assumptions and exposes exciting new research directions. Although the technical details in this talk are focused on heuristic search, the general lessons with which I conclude are relevant to researchers in all branches of A.I.

Speaker Bio:

Professor Emeritus Robert Holte of the Computing Science Department at the University of Alberta is a former editor-in-chief of the journal "Machine Learning" and co-founder and former director of the Alberta Innovates Center for Machine Learning (AICML, now known as Amii). In addition to machine learning, Professor Holte has made seminal contributions to the subfield of A.I. known as single-agent heuristic search, most notably his recent work on bidirectional heuristic search.

Professor Holte was elected a Fellow of the Association for the Advancement of Artificial Intelligence (AAAI) in 2011 and received a Lifetime Achievement Award for his work on heuristic search from the Symposium on Combinatorial Search in 2018. Another Lifetime Achievement Award will be announced at the end of May

]]>

Irrationality of quotient varieties

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

13.05.2019 17:00, Fachgruppe Mathematik, Kollegienhaus der Universität Basel, Petersplatz 1, Hörsaal 117003

Dr. Jitao David Zhang, Dr. Thomas Albrecht, Dr. Volker Herdtweck, F. Hoffmann-La Roche Ltd.

Tags: TAG Events DMI]]>

Principal Scientist, Computational Biology

Pharmaceutical Sciences, Pharma Research and Early Development

Roche Innovation Center Basel

**Dr. Thomas Albrecht**

Senior Scientist, Scientific Solution Engineering & Architecture

Pharma Research and Early Development Informatics

Roche Innovation Center Basel**Dr. Volker Herdtweck**

HR Campus Marketing Manager/University Relations

F. Hoffmann-La Roche Ltd.

Alle Vorträge sind auf Englisch und sind für Studierende der Mathematik, Computer Science und Computational Science geeignet.

Der anschliessende Apéro findet im Foyer der Aula vom Kollegienhaus statt.

]]>

The Local Density Approximation in Density Functional Theory

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Density Functional Theory (DFT) is the main method used in practical computations to approximate solutions of the many-body Schrödinger equation. The main idea is to express everything in terms of the one-particle density instead of the many-body wave function. The Local Density Approximation (LDA) is the simplest nonlinear functional used in this context and it has played a central role in the construction of better empirical approximations since the 60s.

In this talk I will first explain what DFT and LDA are. I will then give the first rigorous justification of the LDA. More precisely, I will show that the exact Levy-Lieb functional of DFT converges to the LDA in the limit of very flat densities. Joint work with Elliott H. Lieb (Princeton) and Robert Seiringer (IST Austria).

Fluid-squeezing singularities for the incompressible Euler equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

I will discuss a new result on the existence of a stationary solution with a fluid-squeezing singularity for the two-fluid incompressible Euler equations. The proof is based on a new set of estimates that permits us to analyze a fluid squeezed by a self-intersecting interface. We will exploit these estimates in the dynamical case and show a local existence result starting from a fluid-squeezing singularity.

]]>The geometry of random walk isomorphisms]]>

The classical random walk isomorphism theorems relate the local time of a random walk to the square of a Gaussian free field. I will present non-Gaussian versions of these theorems, relating hyperbolic and hemispherical sigma models (and their supersymmetric versions) to non-Markovian random walks interacting through their local time. Applications include a short proof of the Sabot-Tarres limiting formula for the vertex-reinforced jump process (VRJP) and a Mermin-Wagner theorem for hyperbolic sigma models and the VRJP. This is joint work with Tyler Helmuth and Andrew Swan. | |

Birational transformations of tetragonal conic bundles

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

In this talk, I will first discuss application of Sarkisov program to the rationality problem of algebraic varieties having conic bundle structures.

Then I concentrate on some special, so-called

The second part of the talk is based on the joint work in progress with V. Shokurov. ]]>

06.05.2019 18:00, Studienfach Mathematik, Spiegelgasse 1, Seminarraum 00.003

Stephanie Meier-Rohr, Softwareentwicklerin, CUBUS AG, Engineering Software

Tags: TAG Events DMI]]>

Im Anschluss daran sind alle herzlich zu einem kleinen Apéro eingeladen.

]]>

Some recent results on the approximation of conservation laws: revisiting the notion of conservation

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

However, this is not the end of the story. All these works use a one dimensional way of thinking: the main player is the normal flux across cell interfaces. In addition there are several excellent numerical methods that do not fit the form of the lax Wendroff theorem.

In that talk, I will introduce a more general setting and show that any reasonable scheme for conservation law can be put in that framework. In addition, I will show that an equivalent flux formulation, with a suitable definition of what is a flux, can be explicitly constructed (and computed), so that any reasonable scheme can be put in a finite volume form.

I will end the talk by showing some applications: how to systematically construct entropy stable scheme, or starting from the non conservative form of a system-say the Euler equations-, how to construct a suitable discretisation. And more.

This is a joint work with P. Bacigaluppi (now postdoc at ETH) and S. Tokareva (now at Los Alamos).

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage.

]]>

Plateau's Problem: The Geometric Measure Theory Approach]]>

On numerical schemes for hyperbolic conservation laws]]>

A distributional approach to fractional Sobolev spaces and fractional variation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Somewhat surprisingly, the first appearance of the concept of a fractional derivative is found in a letter written to de l'Hôpital by Leibniz in 1695. Since then, Fractional Calculus has fascinated generations of mathematicians and several definitions of fractional derivatives have appeared. In more recent years, the fractional operator defined as the gradient of the Riesz potential has received particular attention, since it has revealed to be a useful tool for the study of fractional-order PDEs and fractional Sobolev spaces. In a joint work with G. E. Comi, combining the PDE approach developed by Spector and his collaborators with the distributional point of view adopted by Šilhavý, we introduced new notions of fractional variation and fractional Caccioppoli perimeter in analogy with the classical BV theory. Within this framework, we were able to partially extend De Giorgi’s Blow-up Theorem to sets of locally finite fractional Caccioppoli perimeter, proving existence of blow-ups and giving a first characterisation of these (possibly non-unique) limit sets. In this talk, after a quick overview on Fractional Calculus, I will introduce the main features of the fractional operators involved and then give an account on the main results on the fractional variation we were able to achieve so far.

]]>Real algebraic curves in real minimal del Pezzo surfaces

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Theory of Deep Learning 5: Information theoretic approach to deep learning theory: a test using statistical physics methods]]>

Relying on the heuristic replica method from statistical physics we present an estimator for entropies and mutual informations in models of deep model networks. Using this new tool, we test numerically the relation between generalisation and information. ]]>

Recent methods for solving the high-frequency Helmholtz equation on a regular mesh

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage. ]]>

Flexibility and Rigidity of Isometric Embeddings

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. C^1) than at high regularity (i.e. C^2): for example, it's possible to find C^1 isometric embeddings of the standard 2-sphere into arbitrarily small balls in R^3, and yet, in the C^2 category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture, one might ask if there is a regularity threshold in the Hölder scale which distinguishes these behaviours. In my talk I will give an overview of what is known concerning the latter question.

]]>Theory of Deep Learning 4: Training Neural Networks in the Lazy and Mean Field Regimes]]>

On Compensated Compactness and Hardy Spaces]]>

Theory of Deep Learning 3: Neural Tangent Kernel: Convergence and Generalization of Deep Neural Networks]]>

Multilevel Uncertainty Quantification with Sample-Adaptive Model Hierarchies

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

This is joint work with Gianluca Detommaso (Bath), Tim Dodwell (Exeter) and Jens Lang (Darmstadt).

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage. ]]>

On (Hilbert, Isabelle) and universal pairs]]>

The Dirichlet Problem for the Logarithmic Laplacian

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

I will report on some recent results - obtained in joint work with Huyuan Chen - on Dirichlet problems for the Logarithmic Laplacian Operator, which arises as formal derivative of fractional Laplacians at order s= 0. I will discuss the functional analytic framework for these problems and show how it allows to characterize the asymptotics of principal Dirichlet eigenvalues and eigenfunctions of fractional Laplacians as the order tends to zero. Furthermore, I will discuss necessary and sufficient conditions on domains giving rise to weak and strong maximum principles for the logarithmic Laplacian. If time permits, I will also discuss regularity estimates for solutions to corresponding Poisson problems.

]]>Theory of Deep Learning 2: Over-parametrization in neural networks: an overview and a definition]]>

We will start by reviewing some of the recent literature on the geometry of the loss function, and how SGD navigates the landscape in the OP regime. Then we will see how to define OP by finding a sharp transition described by the models fitting abilities to its training set. Finally, we will discuss how this critical threshold is connected to the generalization properties of the model, and argue that life beyond this threshold is (more or less) as good as it gets. ]]>

Bogoliubov Theory in the Gross-Pitaevskii Limit]]>

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik, TAG Events Studium Informatik]]>

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik, TAG Events Studium Informatik]]>

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik, TAG Events Studium Informatik]]>

Theory of Deep Learning 1: Introduction to the main questions]]>

In this first talk I will introduce the main theoretical questions about deep neural networks:

1. Representation - what can deep neural networks represent?

2. Optimization - why and under what circumstances can we successfully train neural networks?

3. Generalization - why do deep neural networks often generalize well, despite huge capacity?

As a preface I will review the basic models and algorithms (Neural Networks, (stochastic) gradient descent, ...) and some important concepts from machine learning (capacity, overfitting/underfitting, generalization, ...). ]]>

The essential skeletons of pairs and the geometric P=W conjecture

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Linebündeli]]>

]]>

Vektorbündeli]]>

Symmetries of foliation: transverse action

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

I will briefly recall a criterion for the finiteness of the transverse action in the case of algebraically integrable foliations (i.e. foliations whose leaves coincide with the fibres of a fibration). Then I will explain how the presence of certain transverse structures on the foliation allow to recover the same result; in this case, one can study the monodromy of such a structure (which is defined in an analogous way as that of a more familiar (G,X)-structure) and apply factorization results in order to reduce the problem to subvarieties of quotients of the product of unit discs, whose geometry is now quite well understood.

]]>Tags: TAG Events Forschung Mathematik, TAG Events Perlenkolloquium, TAG Events DMI, TAG Events Zahlentheorie]]>

Solution Spaces in Complex Systems Design

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage. ]]>

28.02.2019 14:15 - 28.02.2019 15:15, 00.003 Spiegelgasse 1

Towards effective André-Oort (after Kühne et al.)

Tags: TAG Events DMI, TAG Events Forschung Mathematik, TAG Events Zahlentheorie]]>

Since 2012 various special cases of the André-Oort conjecture has been proved effectively, most notably in the work of Lars Kühne. In my talk I will restrict to the case of the "Shimura variety" C^n and will try to explain on some simple examples how the effective approach of Kühne works.

No previous knowledge about André-Oort conjecture is required, I will give all the necessary background. ]]>

26.02.2019 12:15 - 26.02.2019 14:00, DMI, Spiegelgasse 5, Basel, Raum 05.002

From Data Integration to Knowledge Management

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Alumni Informatik]]>

The time to develop new drugs can be dramatically reduced through intelligent data-integration and re-use. To reduce this time by a factor of 10, Roche Technical Development, an organisation of 2500 colleagues, has embraced a central information integration approach. In this talk I will present our vision and technology platform, give an update on where we are on our journey, and mention some of the barriers we encountered.

Our approach to balance real world needs with accuracy and speed has gained some good success over the course of the last four years for a complex information landscape with hundreds of information entities.

Speaker Bio:

Etzard leads the global Information / Knowledge Management effort in Pharma Technical Development for F. Hoffmann-La Roche in Basel, with a focus on processes and tools for effective knowledge utilisation. Etzard has worked at the interface of the Life- and Computer-Sciences for more than 20 years, in technical, managerial as well as strategic roles.

Before joining Roche, Etzard worked as CIO at the Jackson Lab (a US based genomics research institutes with 1800 employees), and was CTO for the Life Sciences at Hewlett Packard. Etzard has earned academic degrees in Biology, Bio-Informatics and Informatics, with a PhD in Computer Science from ETH Zurich on “A Scalable Architecture for Scientific Databases”.

]]>

A reduced SQP Method for Shape Optimisation of Flow Control Problems

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage. ]]>

Inequalities on Conductors]]>

Tags: TAG Events DMI]]>

**Jubiläumsveranstaltung und Gründung AlumniActuarialScience**

Am 6. Februar 1939 wurde Versicherungslehre an der Universität Basel als selbständiges Examensfach eingeführt. Anlässlich des 80jährigen Bestehens findet am Mittwoch, 6. Februar 2019, im Hörsaal 101 der Alten Universität eine Jubiläumsveranstaltung statt mit Gründung der Fachalumni Actuarial Science.

Alle Interessierten sind herzlich eingeladen. Der Besuch der Veranstaltung ist von der SAV als Weiterbildung anerkannt (1 Credit Point SAV).

**Anmeldung für AlumniEssen**

Für die Vorträge und den anschliessenden Apéro in der Alten Universität ist keine Anmeldung erforderlich.

Das AlumniEssen findet im Restaurant *Zum Isaak* statt und ist für Mitglieder *AlumniActuarialScience* und solche, die es gerne werden wollen. Bitte anmelden bis am 27. Januar 2019 an info@*clutter*AlumniActuarialScience.ch.

*AlumniActuarialScience ***werden**

Mitglied werden in der Fachalumni Actuarial Science können ehemalige Studierende Actuarial Science/Versicherungsmathematik, Dozierende und Emeriti, SAV-Hörer*innen und alle am Studiengang interessierten Privatpersonen und Institutionen.

Weitere Informationen: AlumniActuarialScience.

]]>Cost Partitioning: Raising Prices by Lowering Costs

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik, TAG Events Perlenkolloquium]]>

Dr. Florian Pommerening (Forschungsgruppe Artificial Intelligence / Prof. Dr. Malte Helmert) hat im Rahmen des diesjährigen Dies Academicus den Fakultätspreis der Phil.-Nat. Fakultät für seine Dissertation erhalten.

Im Anschluss an den Vortrag wird ein Apéro offeriert.

]]>Gibbs measures of nonlinear Schrödinger equations and many-body quantum mechanics

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Many time-dependent nonlinear Schrödinger equations admit an invariant Gibbs measure, which is a probability measure on the space of distributions that is left invariant by the time evolution. Such measures have been extensively studied as tool to construct global solutions of time-dependent nonlinear Schrödinger equations with rough initial data. I review some recent progress on deriving these measures in dimensions 1,2,3 as high-temperature limits of many-body quantum mechanics. In one dimension, I also explain how time-dependent correlation functions of the nonlinear Schrödinger equation arise as limits of corresponding quantum many-body correlation functions.

]]>Metastability results for the Navier-Stokes equations and related models

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We study diffusion and mixing in the incompressible Navier-Stokes equations and related scalar models. In this setting, mixing is a purely advective effect which causes a transfer of energy to high frequency. In turn, mixing acts to enhance the dissipative forces, giving rise to what we refer to as enhanced dissipation: this can be understood by the identification of a time-scale faster than the purely diffusive one. This talk is based on two recently obtained results: (1) a general quantitative criterion that links mixing rates (in terms of decay of negative Sobolev norms) to enhanced dissipation time-scales, and (2) a precise identification of the enhanced dissipation time-scale for the Navier-Stokes equations linearized around the Poiseuille flow, along with metastability results and nonlinear transition stability thresholds.

]]>Nonlinear Spectral Decomposition

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage.

]]>Securing a World of Physically Capable Computers

Tags: TAG Events Alumni Informatik, TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik, TAG Events Perlenkolloquium]]>

**Abstract:**

Computer security is no longer about data; it's about life and property. This change makes an enormous difference, and will shake up our industry in many ways. First, data authentication and integrity will become more important than confidentiality. And second, our largely regulation-free Internet will become a thing of the past. Soon we will no longer have a choice between government regulation and no government regulation. Our choice is between smart government regulation and stupid government regulation. Given this future, it's vital that we look back at what we've learned from past attempts to secure these systems, and forward at what technologies, laws, regulations, economic incentives, and social norms we need to secure them in the future.

**Speaker Bio:**

Bruce Schneier is an internationally renowned security technologist, called a security guru by the Economist. He is the author of 14 books -- including the best-seller Click Here to Kill Everybody -- as well as hundreds of articles, essays, and academic papers. His influential newsletter Crypto-Gram and blog Schneier on Security are read by over

250,000 people. Schneier is a fellow at the Berkman Klein Center for Internet and Society at Harvard University; a Lecturer in Public Policy at the Harvard Kennedy School; a board member of the Electronic Frontier Foundation, AccessNow, and the Tor Project; and an advisory board member of EPIC and VerifiedVoting.org. He is also a special advisor to IBM Security and the Chief Technology Officer of IBM Resilient.

]]>

TBA]]>

Equations with complex analytic coefficients

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Geometry inpainting with preserving singularities and curvature

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis external-link-new-window internal link in current>webpage. ]]>

Gaussian Processes for Parametric Modeling of Time Series

Tags: TAG Events Forschung Informatik, TAG Events Studium Informatik]]>

Almost homogeneous curves and surfaces

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

In this talk, I will explain how to classify the pairs (X,G) where X is a curve or a surface and G is a smooth and connected algebraic group acting on X with a dense orbit.

For curves, I will mainly focus on the regular ones, defined over an arbitrary field. Over an algebraically closed field, the "natural" notion of non-singularity is "smoothness". However, over an arbitrary field, the weaker notion of "regularity" is more suitable. I will recall the difference between those two notions and show that there exist regular homogeneous curves which are not smooth.

For surfaces, I will restrict to the smooth ones, defined over an algebraically closed field. The situation is more complicated than for curves. Moreover, new phenomena and several difficulties appear in positive characteristic, and I will highlight them. ]]>

29.11.2018 14:15 - 29.11.2018 15:15

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Tamm's Theorem for log-analytic functions]]>

Finite Energy Weak Solutions of the Navier-Stokes-Korteweg equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In this talk I will present some results concerning the analysis of finite energy weak solutions of the Navier-Stokes-Korteweg equations, which model the dynamic of a viscous compressible fluid with diffuse interface. A general theory of global existence is still missing, however for some particular cases of physical interest I will present results regarding the global existence and the compactness of finite energy weak solutions. The talk is based on a series of joint works with Paolo Antonelli (GSSI - Gran Sasso Science Institute, L’Aquila).

]]>TBA]]>

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

16:15 | Vortrag von Thomas Steiner, Basel: |

17:15 | Apéro mit Präsentation eines neuen Bandes der Euler-Edition durch das Bernoulli-Euler-Zentrum, das Departement Mathematik und Informatik der Universität Basel und Birkhäuser Basel Leonhardi Euleri Opera Omnia, Bd. IVA/8: Herausgegeben von Andreas Kleinert und Thomas Steiner |

18:15 | Vortrag von Andreas Kleinert, Halle/Saale:Eulers hallesche Korrespondenten |

]]>

Probabilistic numerical methods, Bayesian inference and multiscale inverse problems

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

In the second part of the talk, we will discuss a Bayesian approach for inverse problems involving elliptic partial differential equations with multiple scales. Computing repeated forward problems in a multiscale context is computationnally too expensive and we propose a new strategy based on the use of "effective" forward models originating from homogenization theory. Convergence of the true posterior distribution for the parameters of interest towards the homogenized posterior is established via G-convergence for the Hellinger metric. A computational approach based on numerical homogenization and reduced basis methods is proposed for an efficient evaluation of the forward model in a Markov Chain Monte-Carlo procedure.

References:

A. Abdulle, G. Garegnani, Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration, Preprint (2018), submitted for publication.

A. Abdulle, A. Di Blasio, Numerical homogenization and model order reduction for multiscale inverse problems, to appear in SIAM MMS.

A. Abdulle, A. Di Blasio, A Bayesian numerical homogenization method for elliptic multiscale inverse problems, Preprint (2018), submitted for publication.

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage. ]]>

22.11.2018 14:15 - 22.11.2018 15:15

On bounded automorphisms of fields with operators

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Adaptive Eigenspace Inversion for Breast Tumour Detection ]]>

Propagation of regularity and mixing estimates for solutions of the incompressible continuity equation with Sobolev vector field

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Since the work by DiPerna and Lions (1989) the continuity and transport equation under mild regularity assumptions on the vector field have been extensively studied, becoming a florid research field. The applicability of this theory is very wide, especially in the study of partial differential equations and very recently also in the field of non-smooth geometry.

The aim of this talk is to give an overview of the quantitative side of the theory initiated by Crippa and De Lellis. We address the problem of mixing and propagation of regularity for solutions to the continuity equation drifted by Sobolev fields. The problem is well understood when the vector field enjoys a Sobolev regularity with integrability exponent p>1 and basically nothing is known (at the quantitative level) in the case p=1.

We present sharp regularity estimates for the case p>1 and new attempts to attack the challenging question in the case p=1. This is a join work with Quoc-Hung Nguyen.

]]>Local law and eigenvector delocalization for supercritical Erdos-Renyi graphs]]>

Joint work with Yukun He and Matteo Marcozzi.

]]>Hyperkähler manifolds and their Betti numbers

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Optimal transport in seismic imaging based on full waveform inversion

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis external-link-new-window internal link in current>webpage.

]]>MOONSTAR - Sentinel Lymph Node Fingerprinting]]>

Oriented first passage percolation on the hypercube]]>

Positivity, Graphs and Unknotting

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Wavenumber-Explicit Analysis for High-Frequency Maxwell Equations

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

This talk comprises joint work with Prof. Markus Melenk, TU Wien.

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage.

]]>08.11.2018 16:15 - 08.11.2018 18:00, DMI, Spiegelgasse 1, Basel, Seminarraum 00.003 im EG

Decentralized Collective Learning for Self-managed Sharing Economies

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Alumni Informatik]]>

Abstract:

The Internet of Things equips citizens with phenomenal new means for online participation in sharing economies. When agents self-determine options from which they choose, for instance their resource consumption and production, while these choices have a collective system-wide impact, optimal decision-making turns into a combinatorial optimization problem known as NP-hard. In such challenging computational problems, centrally managed (deep) learning systems often require personal data with implications on privacy and citizens’ autonomy. This paper envisions an alternative unsupervised and decentralized collective learning approach that preserves privacy, autonomy and participation of multi-agent systems self-organized into a hierarchical tree structure.

Remote interactions orchestrate a highly efficient process for decentralized collective learning. This disruptive concept is realized by I-EPOS, the Iterative Economic Planning and Optimized Selections, accompanied by a paradigmatic software artifact. Strikingly, I-EPOS outperforms related algorithms that involve non-local brute-force operations or exchange full information. This paper contributes new experimental findings about the influence of network topology and planning on learning efficiency as well as findings on techno-socio-economic trade-offs and global optimality. Experimental evaluation with real-world data from energy and bike sharing pilots demonstrates the grand potential of collective learning to design ethically and socially responsible participatory sharing economies.

]]>

08.11.2018 14:15 - 08.11.2018 15:15

Solving polynomial-exponential equations.

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

$$e^z+e^{\root 9 \of {1-z^9}}=1$$

one approach uses theta functions on ${\bf C}^{28}$. ]]>

Primitive root problems]]>

Cusp Universality for Wigner-type Random Matrices]]>

06.11.2018 12:15 - 06.11.2018 13:30, DMI, Spiegelgasse 5, Basel, Seminarraum 05.002 im 5. OG

Modeling and Individualizing Learning in Computer-Based Environments

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Alumni Informatik]]>

Abstract:

Learning technologies are becoming increasingly important in today's education. This includes game-based learning and simulations, which produce high volume output, and MOOCs (massive open online courses), which reach a broad and diverse audience at scale. The users of such systems often are of very different backgrounds, for example in terms of age, prior knowledge, and learning speed. Adaptation to the specific needs of the individual user is therefore essential. In this talk, I will present two of my contributions on modeling and predicting student learning in computer-based environments with the goal to enable individualization. The first contribution introduces a new model and algorithm for representing and predicting student knowledge. The new approach is efficient and has been demonstrated to outperform previous work regarding prediction accuracy. The second contribution introduces models, which are able to not only take into account the accuracy of the user, but also the inquiry strategies of the user, improving prediction of future learning. Furthermore, students can be clustered into groups with different strategies and targeted interventions can be designed based on these strategies. Finally, I will also describe lines of future research.

]]>Around a big mapping class group

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

]]>

Transparent boundary conditions for sound propagation in human lungs, modelled by fractal trees

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

The construction of such transparent conditions relies on the approximation of the Dirichlet-to-Neumann (DtN) operator, whose symbol is a meromorphic function that satisfies a certain non-linear functional equation. We present two approaches to approximate the DtN in the time domain, alternative to the low-order absorbing boundary conditions, which appear inefficient in this case.

The first approach stems from the use of the convolution quadrature (cf. [Lubich 1988], [Banjai, Lubich, Sayas 2016]), which consists in constructing an exact DtN for a semi-discretized in time problem. In this case the combination of the explicit leapfrog method for the volumic terms and the implicit trapezoid rule for the boundary terms leads to a second-order scheme stable under the classical CFL condition.

The second approach is motivated by the Engquist-Majda ABCs (cf. [Engquist, Majda 1977]), and consists in approximating the DtN by local operators, obtained from the truncation of the meromorphic series which represents the symbol of the DtN. We show how the respective error can be controlled and provide some complexity estimates.

This is a joint work with Patrick Joly (INRIA, France) and Adrien Semin (TU Darmstadt, Germany).

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage.

]]>01.11.2018 14:15 - 01.11.2018 15:15

]]>

Fields of definition and abelian varieties]]>

High-dimensional Gaussian fields with isotropic increments seen through spin glasses]]>

Mathematics in drug discovery: a practitioner’s view

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Jitao David Zhang was a Marie-Curie Fellow at European Bioinformatics Institute (2007-2008) and an International PhD Programm Fellow at German Cancer Research Center (2008-2011). He obtained the doctorate degree in computational biology and biostatistics in 2011 and in that year joined Pharma Research and Early Development (pRED), the research unit of F. Hoffmann-La Roche AG in Basel, Switzerland. He supports early drug-discovery projects, develops algorithms and software for data analysis and interpretation, and collaborates to devise new technologies and platforms. His research interests include biological data modelling and integration, biological network analysis, molecular phenotyping, and applied machine learning in disease understanding and preclinical drug discovery.

]]>Spline curves in Riemannian Shape Spaces

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Die AlumniComputerScience werden im Anschluss an das DMI-Kolloquium mit einem Apéro eröffnet. Sie sind herzlich dazu eingeladen.

Tags: TAG Events Alumni Informatik]]>

18.10.2018 17:15 - 18.10.2018 19:00, Hörsaal 001, Kollegienhaus, Petersplatz 1, Basel

Öffentliche Antrittsvorlesungen

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik, TAG Events Alumni Informatik, TAG Events Perlenkolloquium]]>

Prof. Dr. Jiří Černý, Professor für Wahrscheinlichkeitstheorie*Random Walk Percolation and Level Sets of Random Fields*

Prof. Dr. Julia Vogt, Professorin für Adaptive Systems and Medical Data Science*Machine Learning for Clinical Data Analysis and Precision Medicine*

Im Anschluss an die Vorträge findet das Kickoff der Alumni Computer Science statt und es wird ein Apéro offeriert. Der Anlass ist öffentlich.

]]>Talks to present past and current work.

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

On variational methods in Fourier analysis

Tags: TAG Events Forschung Mathematik]]>

Johann Bernoulli im Prioriätsstreit zwischen Leibniz und Newton

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

04.10.2018 14:15 - 04.10.2018 15:15

On Goormaghtigh's equation

Tags: TAG Events Zahlentheorie, TAG Events Forschung Mathematik]]>

\begin{equation}\label{eq}

\frac{x^m-1}{x-1} = \frac{y^n-1}{y-1}, \; \; y>x>1, \; m > n > 2.

\end{equation}

There are two known solutions $(x, y,m, n)=(2, 5, 5, 3), (2, 90, 13, 3)$ and it is believed that these are the only solutions. It is not known if this equation has finitely or infinitely many solutions, and not even if that is the case if we fix one of the variables. It is known that there are finitely many solutions if we fix any two variables. Moreover, there are effective results in all cases, except when the two fixed variables are the exponents $m$ and $n$. If the fixed $m$ and $n$ additionally satisfy $\gcd(m-1, n-1)>1$, then there is an effective finiteness result. My co-authors and me showed that if $n \geq 3$ is a fixed integer, then there exists an effectively computable constant $c (n)$ such that $\max \{ x, y, m \} < c (n)$ for all $x, y$ and $m$ that satisfy Goormaghtigh's equation with $\gcd(m-1,n-1)>1$. In case $n \in \{ 3, 4, 5 \}$, we solved the equation completely, subject to this non-coprimality condition. ]]>

Talks to present past and current work.

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Immanuel van Santen will speak about „Embeddings and tame automorphisms in affine geometry",

Anne Lonjou will explain some link between "Cremona group and geometric group theory", and

Jérémy Blanc will present us "Birational geometry of surfaces and threefolds".

]]>28.09.2018 12:15 - 28.09.2018 14:00, Computer Science, Spiegelgasse 1, Raum 00.003

Medical Video Analytics

Tags: TAG Events Forschung Informatik, TAG Events DMI]]>

**Abstract:**In hospitals all around the world, medical multimedia information systems have gained high importance over the last few years. One of the reasons is that an increasing number of interventions is performed in a minimally invasive way. These endoscopic inspections and surgeries are conducted with a tiny camera – the endoscope – which enables clinicians to control the intervention via an external display. Apart from the viewing purpose, the video signal can also be recorded and used for post-procedural scenarios, such as communicating operation techniques (i.e., training and teaching), planning future interventions, and medical forensics and analytics. The problem, however, is the sheer amount of unstructured video data that is added to the multimedia archive on a daily basis. Without proper management and content analytics the videos cannot be used efficiently by clinicians. In this talk I will summarize our recent investigations in this challenging research field and conclude on the achieved results.

**Bio:**Dr. Klaus Schöffmann is an Associate Professor in the Distributed Multimedia Systems research group at the Institute of Information Technology (ITEC) at Klagenfurt University, Austria. He received his PhD in 2009 and his habilitation (venia docendi) in 2015, both in computer science and from Klagenfurt University. His research focuses on video analytics and interactive multimedia systems, particularly in the medical domain. He has co-authored more than 100 publications on various topics in multimedia, inclusive of more than 25 on different aspects of medical multimedia systems. He has co-organized several international conferences, workshops, and special sessions in the field of multimedia. Furthermore, he is co-founder of the Video Browser Showdown (VBS) – an international live evaluation competition of interactive video search. He is a member of the IEEE and the ACM, and a regular reviewer for international conferences and journals in the field of multimedia. Klaus Schöffmann teaches various courses in computer science, including mobile app development, video retrieval, distributed multimedia systems, and operating systems.

Tags: TAG Events Forschung Informatik]]>

27.09.2018 14:15 - 27.09.2018 15:15

Extreme values of the Riemann Zeta function, and log-correlated Gaussian fields ]]>

From Biology to Polynomials and Beyond: A Brief Look at Algebraic Statistics

Tags: TAG Events Forschung Mathematik]]>

Talks to present past and current work.

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Julia will speak about "A_k-singularities of plane curves of fixed bidegree".

Egor will answer to "What transformation groups in algebraic, differential and metric geometry have in common?".

Philipp will speak about "Algebraic Statistics: Gaussian Mixtures and Beyond".

]]>Tags: TAG Events Forschung Mathematik, TAG Events Perlenkolloquium]]>

Wasserstein metric based full waveform inversion

Tags: TAG Events Forschung Mathematik]]>

The Ginibre ensemble and Gaussian multiplicative chaos]]>

(Joint work in progress with Paul Bourgade and Guillaume Dubach).

]]>Ubiquity of phases in some percolation models with long-range correlations

Tags: TAG Events Forschung Mathematik]]>

This talk is based on joint works with A. Prévost (Köln) and P.-F. Rodriguez (Bures-sur-Yvette).

]]>13.07.2018 10:45, Fabrizio Barroero, Philipp Habegger, Alte Universität U101

Tags: TAG Events Forschung Mathematik, TAG Events Zahlentheorie, TAG Events DMI]]>

03.07.2018 18:30 - 03.07.2018 19:30, Congress Center Basel, Montreal Room

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik]]>

Emerging real-world graph problems include: detecting and preventing disease in human populations; revealing community structure in large social networks; and improving the resilience of the electric power grid. Unlike traditional applications in computational science and engineering, solving these social problems at scale often raises new challenges because of the sparsity and lack of locality in the data, the need for research on scalable algorithms and development of frameworks for solving these real-world problems on high performance computers, and for improved models that capture the noise and bias inherent in the torrential data streams. In this talk, Bader will discuss the opportunities and challenges in massive data-intensive computing for applications in social sciences, physical sciences, and engineering.

David Bader is Professor and Chair of the School of Computational Science and Engineering at Georgia Institute of Technology, and is regarded as one of the world’s leading experts in data sciences. His interests are at the intersection of high performance computing (HPC) and real-world applications, including cybersecurity, massive-scale analytics, and computational genomics. Bader has co-authored over 200 articles in peer-reviewed journals and conferences, and is an associate editor for high-impact publications including IEEE Transactions on Computers, ACM Transactions on Parallel Computing, and ACM Journal of Experimental Algorithmics. He is a Fellow of the IEEE and AAAS, and has served on a number of advisory committees in scientific computing and cyber-infrastructure, including the White House's National Strategic Computing Initiative. Bader has served as a lead scientist in several DARPA programs and is a co-founder of the Graph500 list, a rating of "Big Data" computing platforms. He was recognized as a “Rock Star of HPC” by InsideHPC and as HPCwire's “People to Watch” in 2012 and 2014.

More details:

pasc18.pasc-conference.org/program/public-lecture/

]]>

02.07.2018 00:00 - 04.07.2018 00:00, Computer Science, Congress Center Basel

Tags: TAG Events DMI, TAG Events Forschung Informatik, TAG Events Forschung Mathematik]]>

The PASC18 theme is

The PASC18 technical program (pasc18.pasc-conference.org/program/schedule/) is organized around eight scientific domains: Chemistry and Materials, Climate and Weather, Computer Science and Applied Mathematics, Emerging Domains in HPC, Engineering, Life Sciences, Physics, and Solid Earth Dynamics. Over the course of three full days, the program includes, technical sessions with keynotes, panels, minisymposia, peer-reviewed papers and poster sessions. Full papers are published in the ACM Digital Library.

We look forward to advancing scientific computing with you at the Basel Congress Center on July 2-4!

]]>

Tags: TAG Events Forschung Mathematik, TAG Events Perlenkolloquium]]>

21.06.2018 10:00 - 21.06.2018 12:00, Computer Science, Spiegelgasse 1, Seminar Room 00.003 (ground floor)

Advances in the TAU Performance System and the Need for Dynamic Performance Introspection, In Situ Analysis, and Adaptation

Tags: TAG Events Forschung Informatik, TAG Events DMI]]>

**Abstract:** Since the beginning of ``high-performance'' parallel computing, observing

and analyzing performance for purposes of finding bottlenecks and

identifying opportunities for improvement has been at the heart of

delivering the performance potential of next-generation scalable systems.

Interestingly, it is the ever-changing parallel computing landscape that is

the main driver of requirements for parallel performance technology and the

improvements necessary beyond the current state-of-the-art. Indeed, the

development and application of our TAU Performance System over many years

largely follows an evolutionary path of addressing measurement and analysis

problems in new parallel machines and programming environments.

However, the outlook to future parallel systems with high degrees of

concurrency, heterogeneous components, dynamic runtime environments,

asynchronous execution, and power constraints suggests a new perspective

will be needed on the role of performance observation and analysis in

respect to tool technology integration and performance optimization

methods. The reliance on post-mortem analysis of application-level

("1st person") performance measurements is prohibitive for

exascale-class machines because of the performance data volume, the

primitive basis for performance data attribution, and the fundamental

problem of performance variation that will exist. Instead, it will be

important to provide introspection support across the exascale software

stack to understand how system ("3rd person") resources are used during

execution. Furthermore, the opportunity to couple a global performance

introspection capability (a "performance backplane") with online

performance decision analytics inspires the concept of an autonomic

performance system that can feed back policy-based decisions to guide

the computation to better states of execution.

The talk will explore these issues by giving a brief retrospective on

performance tool evolution, setting the stage for current research

projects where a new performance perspective is being pursued. It will

also speculate on what might be included in next-generation parallel

systems hardware, specifically to make the exascale machines more

performance-aware and dynamically-adaptive. **Speaker Bio: **Allen D. Malony is a Professor in the Department of Computer and

Information Science at the University of Oregon (UO) where he directs

parallel computing research projects, notably the TAU parallel

performance system project. He has extensive experience in performance

benchmarking and characterization of high-performance computing systems,

and has developed performance evaluation tools for a range of parallel

machines during the last 30 years. Malony is also interested in

computational and data science. He is the Director of the new Oregon

Advanced Computing Institute for Science and Society (OACISS) at UO.

Malony was awarded the NSF National Young Investigator award, was a

Fulbright Research Scholar to The Netherlands and Austria, and received

the Alexander von Humboldt Research Award for Senior U.S. Scientists by

the Alexander von Humboldt Foundation. Last year he was the

Fulbright-Tocqueville Distinguished Chair to France. Recently, he was

award the Fulbright for the Future by the Franco-Americaine Fulbright

Commission. Malony is the CEO of ParaTools, Inc., which he founded with

Dr. Sameer Shende in 2004. ParaTools SAS is a French company they

started in 2014, and is wholly-owned company by ParaTools, Inc.

ParaTools specializes in performance analysis and engineering, HPC

applications and optimization, and parallel software, hardware, and

tools.

How and why to pack in big dimensions

Tags: TAG Events Forschung Mathematik, TAG Events Forschung Informatik, TAG Events DMI, TAG Events Perlenkolloquium]]>

In this talk we will speak about packing problems in multidimensional spaces. We will give an overview of this interesting class of mathematical questions and recent progress in the area. Also we will explain the importance of good packing configurations in applications such as internet, telecommunication, and data storage.

The talk is part of the annual meeting 2018 of the Swiss Mathematical Society.

]]>Speakers: Nicolas Bergeron, Gal Binyamini, Valentin Blomer, Ana Caraiani, Laura DeMarco

Tags: TAG Events Forschung Mathematik]]>

On energy-stable discontinuous Galerkin approximations for scattering problems in complex elastic media with adaptive curvilinear meshes

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

The maximal number of lines going through the same point on del Pezzo surfaces of degree one]]>

Abelian quotients of the Cremona groups

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Localization of orthonormal functions in spectral clusters

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Localization of eigenfunctions via an effective potential

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Lu = -div(A∇u) + Vu

on a Lipschitz domain Ω and, more generally, on a manifold with or without boundary. The eigenfunctions of L are often localized, as a result of disorder of the potential V , the matrix of coefficients A, irregularities of the boundary, or all of the above. In earlier work, Filoche and Mayboroda introduced the function u solving Lu = 1, and showed numerically that it strongly reflects this localization. Here, we deepen the connection between the eigenfunctions and this landscape function u by proving that its reciprocal 1/u acts as an effective potential. The effective potential governs the exponential decay of the eigenfunctions of the system and delivers information on the distribution of eigenvalues near the bottom of the spectrum.

]]>Optimal transport in seismic imaging based on full waveform inversion

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

24.05.2018 15:00 - 24.05.2018 16:00, Computer Science, Spiegelgasse 1, Room 05.013, 5th floor

From Location to Location Pattern Privacy

Tags: TAG Events Forschung Informatik]]>

**Abstract:** Location privacy is getting increased attention due to mass use of Location Based Services (LBSs). Location privacy aims at protecting individuals' exact location from LBS providers. For this purpose, sharing coarse locations respecting users' location privacy profiles are commonly applied. The problem gets more complicated especially in urban areas where user movements are restricted on roads and the visited places are semantically annotated like bars, night clubs etc. This way location can act as an intrusive inference on people's personal preferences and habits. So, location privacy is not confined to privacy of location itself. Moreover, any sensitive pattern in users' trajectories can be resurfaced by data mining.

In this talk, especially for urban area mobility, I will give how location privacy profiles can be defined and maintained w.r.t. possible attack models. Then, I will introduce temporally annotated sequences as a means to define sensitive location patterns. Finally, a sensitive location pattern suppression mechanism running in online stream fashion of LBS access will be detailed. **Speaker Bio:** Osman Abul is currently an associate professor of computer science at TOBB University of Economics and Technology, Ankara, Turkey. He received his PhD degree in computer engineering from Middle East Technical University, Ankara, Turkey. He held visiting posts in University of Calgary, Norwegian University of Science and Technology, and Italian Institute of Information Science and Technology. His research interests include data mining, data privacy and bioinformatics.

On the N-body problem and the Vlasov-Poisson equation]]>

Automorphism groups of Danielewski surfaces (TALK CANCELLED)

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Machine Learning Driving Innovative Computing Concepts

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

The study of dynamical systems has a long history. Many people consider Henri Poincaré as the founder (at the end of the 19th century) of the modern theory of dynamical systems. Further important contributions at the beginning of the 20th are due to George David Birkhoff, Gaston Julia and Pierre Fatou.

In the talk we will discuss some aspects of the theory of dynamical systems with a view toward arithmetic. As an example we will show that Birkhoff's multiple recurrence Theorem can be used to provide an alternative proof of van der Waerden's Theorem on arithmetic progressions. We will also show that Julia sets are useful to understand the dynamic given by a rational function. ]]>

An introduction to Cayley-Bacharach theorems]]>

Complex plane curves, their intersection with round spheres, and knot concordance

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Noetherianity up to conjugation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

An Adaptive Multiscale Approach for Electronic Structure Methods

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Two-level Domain Decomposition preconditioners for Maxwell equations

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

[1] I. G. Graham, E. A. Spence, and E. Vainikko. Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption. Mathematics of Computation, 86(307):2089–2127, 2017.

]]>Percolation on the Erdös-Renyi model]]>

Isomorphisms between complements of unicuspidal curves in the projective plane

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The Mordell-Weil Theorem and the rank of elliptic curves]]>

Rational simple connectedness for Fano varieties

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In the current joint project with Laurent Gruson and Nicolas Perrin, we study some examples of Fano varieties in low dimension via explicit birational methods. ]]>

Mesh Refinement for T-splines in any dimension

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

As an outlook to future work, we outline an approach for the handling of zero knot intervals and multiple lines in the interior of the domain, which are used in CAD applications for controlling the continuity of the spline functions, and we also sketch basic ideas for the local refinement of two-dimensional meshes that do not have tensor-product structure.

]]>SPDE's and regularity structures]]>

Some affine plane bundles over the punctured affine plane

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The famous Dolgachev-Weisfeiler conjecture predicts that such fibrations are in fact isomorphic to the trivial bundle. We will show that this holds true in some particular examples. For instance, we will recover a result of Drew Lewis which states that the $\mathbb{A}^2$-fibration induced by the second Vénéreau polynomial is trivial.

Our proof is inspired by a previous work of Kaliman and Zaidenberg and consists in first showing that the considered fibrations have a fiber bundle structure when restricted over the punctured affine plane.

This is a joint work in progress with Jérémy Blanc. ]]>

Optimal adaptivity in finite and boundary element methods

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

In this talk, we first consider an adaptive FEM with hierarchical splines of arbitrary degree for linear elliptic PDE systems of second order with Dirichlet boundary condition for arbitrary dimension d≥2. We assume that the problem geometry can be parametrized over the d-dimensional unit cube. We propose a refinement strategy to generate a sequence of locally refined meshes and corresponding discrete solutions. Adaptivity is driven by some weighted-residual a posteriori error estimator. In [1], we proved linear convergence of the error estimator with optimal algebraic rate.

Next, we consider an adaptive BEM with hierarchical splines of arbitrary degree for weakly-singular integral equations of the first kind that arise from the solution of linear elliptic PDE systems of second order with constant coefficients and Dirichlet boundary condition. We assume that the boundary of the geometry is the union of surfaces that can be parametrized over the unit square. Again, we propose a refinement strategy to generate a sequence of locally refined meshes and corresponding discrete solutions, where adaptivity is driven by some weighted-residual a posteriori error estimator. In [2], we proved linear convergence of the error estimator with optimal algebraic rate. In contrast to prior works, which are restricted to the Laplace model problem, our analysis allows for arbitrary elliptic PDE operators of second order with constant coefficients.

Finally, for one-dimensional boundaries, we investigate an adaptive BEM with standard splines instead of hierarchical splines. We modify the corresponding algorithm so that it additionally uses knot multiplicity increase which results in local smoothness reduction of the ansatz space. In [3], we proved linear convergence of the employed weighted-residual error estimator with optimal algebraic rate.

[1] G. Gantner, D. Haberlik, and Dirk Praetorius, Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines. Math. Mod. Meth. in Appl. S., Vol. 27, 2017.

[2] G. Gantner, Optimal adaptivity for splines in finite and boundary element methods, PhD thesis, TU Wien, 2017.

[3] Michael Feischl, Gregor Gantner, Alexander Haberl, and Dirk Praetorius. Adaptive 2D IGA boundary element methods. Eng. Anal. Bound. Elem., Vol. 62, 2016.

]]>Tags: TAG Events Forschung Mathematik, TAG Events Perlenkolloquium]]>

Automorphisms of pointless surfaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We will also discuss some particular types of surfaces with interesting automorphism groups, including Severi-Brauer surfaces. ]]>

Shape Optimization by Finite Elements]]>

Non-rationality of conic-bundles over IP^3

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

27.02.2018 12:15 - 27.02.2018 14:00, Computer Science, Spiegelgasse 5, Seminarraum 05.002, 5. OG

The Pathfinding Engine of Dragon Age: Origins

Tags: TAG Events Forschung Informatik]]>

**Abstract:** What does it take to build a high-quality pathfinding engine? One might think that pathfinding in games is a simple case of using A*, which finds shortest paths. But, in practice, there are many other considerations for finding high-quality paths quickly in dynamic environments. This talk will give an overview of the techniques required to build the pathfinding engine of Dragon Age: Origins. Five iterations of improvements will be presented, starting from basic pathfinding approaches, and moving to a final system that creates high-quality, smooth paths. To conclude, we will discuss open challenges in pathfinding and what it would take to create a pathfinding system that finds human-quality paths.

**Speaker Bio:** Nathan Sturtevant is an Associate Professor in the Computer Science Department at the University of Denver. His scientific research focuses on search in Artificial Intelligence. This includes work on heuristic and combinatorial search for single and multiple agents, including bidirectional search, automated abstraction, heuristics, refinement search, search for game design, heuristic learning, inconsistent heuristics, cooperative search, large-scale and parallel search.

Particular applications include pathfinding and planning in memory-constrained real-time environments (e.g. commercial video games) as well as algorithms for building and using memory-based heuristics via large-scale search. Other work considers theoretical and practical issues in games with more than two players, including opponent modeling, learning, and imperfect information.

Cremona contractibility]]>

Birational geometry of pairs

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Sparse grids in optimal control]]>

Regularity of free boundaries in obstacle problems for integro-differential operators

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We present a brief overview of the regularity theory for free boundaries in different obstacle problems. We describe how a monotonicity formula of Almgren plays a central role in the study of the regularity of the free boundary in some of these problems. Finally, we explain new strategies which we have recently developed to deal with cases in which monotonicity formulas are not available.

]]>Quantitative estimates of propagation of chaos for stochastic systems with singular interactions

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction kernel in the negative Sobolev space W^{-1,∞}, thus including the Biot-Savart law and the point vortices dynamics for the 2d incompressible Navier-Stokes.

Tidal energy in Newtonian two-body motion

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In this work, which is based on an essential linear analysis by Christodoulou, we study the tidal energy for the motion of two gravitating incompressible fluid balls with free boundaries, obeying the Euler-Poisson equations. The orbital energy is defined as the mechanical energy of the center of mass of the two bodies. When the fluids are replaced by point masses, according to the classical analysis of Kepler and Newton, the conic curve describing the trajectories of the bodies is a hyperbola when the orbital energy is positive and an ellipse when the orbital energy is negative. If the point masses are initially very far, then the orbital energy, which is conserved in the case of point masses, is positive corresponding to hyperbolic motion. However, in the motion of fluid balls the orbital energy is no longer conserved, as part of the conserved energy is used in deforming the boundaries of the bodies. This energy is called the tidal energy. If the tidal energy becomes larger than the total energy during the evolution, the orbital energy must change its sign, signaling a qualitative change in the orbit of the bodies. We will show that under appropriate conditions on the initial configuration this change of sign occurs. Our analysis relies on an a-priori estimates which we establish up to the point of closest approach.

(This is a joint work with Sohrab Shahshahani from UMass Amherst.)

]]>McKay Correspondence]]>

Dirac operators with magnetic links

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We consider Dirac operators on the 3-sphere with singular magnetic fields which are supported on links, that is on one-dimensional manifolds which are diffeomorphic to finitely many copies of S^{1}. Each connected component carries a flux 2πα which exhibits a 2π-periodicity, just like Aharonov-Bohmsolenoids in the complex plane. We study the kernel of such operators through the spectral flow of loops corresponding to tuning some flux from 0 to 2π, that is the number of eigenvalues crossing 0 along the loop (counted algebraically). It turns out that the spectral flow is generically non-zero and depends on the shape of the curves and their linking number. Through the stereographic projection the result extends to R^{3}. And then by smearing out the magnetic fields we obtain new solutions (ψ,A) to the zero-mode equation on R^{3}:

σ·(-i∇+A)=0,

(ψ,A) ∈ H^{1}(R^{3})^{2} × \dot{H}^{1}(R^{3})^{3 }∩ L^{6}(R^{3})^{3},

where σ=(σ)_{j=1...3} denotes the family of the Pauli matrices, A is the magnetic potential associated to the magnetic field ∇×A, and σ⋅(-i∇+A) is the corresponding Dirac operator in R^{3}.

(Joint work with Fabian Portmann and Jan Philip Solovej)

]]>Signature morphisms of the Cremona group of the plane

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

External boundary control of the motion of a rigid body immersed in a perfect two-dimensional fluid

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We consider the motion of a rigid body due to the pressure of a surrounded two-dimensional irrotational perfect incompressible fluid, the whole system being confined in abounded domain with an impermeable condition on a part of the external boundary. Thanks to an impulsive control strategy we prove that there exists an appropriate boundary condition on the remaining part of the external boundary (allowing some fluid going in and out the domain) such that the immersed rigid body is driven from some given initial position and velocity to some final position and velocity in a given positive time, without touching the external boundary. The controlled part of the external boundary is assumed to have a nonvoid interior and the final position is assumed to be in the same connected component of the set of possible positions as the initial position.

]]>Aspects of Adaptive Galerkin FEM for random PDEs

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Better bounding]]>

Fibre-like Fano manifolds: a bestiary

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Patterns formation for minimizers of a local/non-local interaction functional in general dimension

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We study a functional consisting of a perimeter term and a non-local term which are in competition, both in the discrete and continuous setting.In the discrete setting such functional was introduced by Giuliani, Lebowitz, Liebe and Seiringer. For both the continuous and discrete problem, we show that the global minimizers are exact periodic stripes. One striking feature of the functionals is that the minimizers are invariant under a smaller group of symmetries than the functional itself. In the continuous setting, to our knowledge this is the first example of a model with local/nonlocal terms in competition such that the functional is invariant under permutation of coordinates and the minimizers display a pattern formation which is one dimensional. Such behaviour for a smaller range of exponents in the discrete setting had been already shown,using different techniques. This is a joint work with E. Runa.

]]>A Mixed Finite-Element Method for Gas Transport on Pipeline Networks

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

The beauty of elliptic curves]]>

Characterisation of varieties by their automorphisms

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Let X be a quasi-affine irreducible variety such that Aut(X) \simeq Aut(A

(1) X is a Q-acyclic open subset of a smooth affine rational variety, and dim(X) is a most equal to n;

(2) X is toric and dim(X) is at least equal to n. After giving a brief history on some related results that concern the characterisation of geometric objects via their automorphisms, we give the key ideas of the proof of our main result. ]]>

The Porous Medium Equation with Large Initial Data on Negatively Curved Riemannian Manifolds

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We discuss existence and uniqueness of very weak solutions of the Cauchy problem for the porous medium equation on Cartan–Hadamard manifolds satisfying suitable lower bounds on Ricci curvature, with initial data that can grow at inﬁnity at a prescribed rate, that depends crucially on the curvature bounds. Furthermore, we give a precise estimate for the maximal existence time, and we show that in general solutions do not exist if the initial data grow at inﬁnity too fast. Such results have been recently obtained jointly with G. Grillo and M. Muratori.

]]>Introduction to Deep Reinforcement Learning for Non-Machine-Learners]]>

On birational transformations of P3 of low degree

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

SQP Methods for Shape Optimization Based on Weak Shape Hessians

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

The talk introduces shape optimization as a special sub-class of PDE constraint optimization problems. The main focus here will be on generating Newton-like methods for large scale applications. The key for this endeavor is the derivation of the shape Hessian, that is the second directional derivative of a cost functional with respect to geometry changes in a weak form based on material derivatives instead of classical local shape derivatives. To avoid human errors, a computer aided derivation system is also introduced.

The methodologies are tested on problem from fluid dynamics and geometric inverse problems.

]]>Matrix Factorizations and Chern classes for modules with (eventually) periodic resolutions]]>

Geometry of the fibres of some integrable systems]]>

Commensurating actions of birational groups

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Small G-varieties

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

An affine G-variety X is called

A striking consequence is the following result.

Theorem. Let n > 4. Then a smooth $\SL_n$-variety of dimension d < 2n-2 is an $\SL_n$-vector bundle over a smooth variety of dimension d-n. There are also interesting applications to actions of the affine group $\Aff_n$. This was the starting point of this joint work with with Andriy Regeta and Susanna Zimmermann. ]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Optimizing strategies for releasing sterile mosquitoes]]>

Cremona group and hyperbolic spaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Del Pezzo fibrations in positive characteristic

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Some remarks on Poonen's conjecture

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We are interested in cycles of φ

An extension problem for Riemannian metrics

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The problem of extending a given metric on a finite three dimensional domain to one which is asymptotically flat and which satisfies the constraint equations of general relativity was proposed by Robert Bartnik. He proposed that the minimal mass of such an extension would be a measure of the quasi-local mass of the domain and this is called the Bartnik mass. In this talk we will describe this problem and recent results on it including a comparison of the Bartnik mass to other quasi-local mass notions.

]]>A fully non-linear flow with surgeries for 2-convex hyper-surfaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The lecture describes joint work with Simon Brendle on the motion of closed hyper surfaces in a Riemannian manifold, on which the sum of any two principal curvatures is positive at all points. We exhibit a fully non-linear, parabolic choice of deformation law that preserves this curvature condition and allows only neck-like singularities which can be overcome by finitely many surgeries. The lecture explains the analytical techniques involved and sharp geometric conclusions made possible by this flow.

]]>Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

A Family of 65-Nodal Sextics]]>

Pseudotrees and Not Getting Slapped Too Often]]>

Quantum Machine Learning (QML)

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Stochastic two-dimensional decomposition of high-dimensional solution spaces for robust design]]>

Finite Energy Weak Solutions of the Quantum Navier-Stokes equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In this talk I will present a result concerning the global existence of finite energy weak solutions of the quantum Navier-Stokes equations. The novelty of the result is that we are able to consider the vacuum in the definition of weak solutions. The main tools are a new formulation of the equations which allows us to get an additional a priori estimate to prove compactness and a non trivial choice of the approximation system consistent with the a priori estimates.

This is a joint work with Paolo Antonelli (GSSI)

]]>Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Rational and non-rational varieties

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

For example, non-singular plane cubic curves (elliptic curves) cannot be rationally parametrized. In dimension one and two, the problem of existence of such parametrization is completely solved.

In higher dimensions, the picture is less clear. In this talk, I will survey know results and open problems in this direction.

]]>Local time discretisation based on transmission problem for linear wave equations: construction and analysis

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Igusa quartic and and Wiman-Edge sextics

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Arnaud Beauville proved that all but four of these quartic threeffolds are irrational. Later Cheltsov and Shramov proved that the remaining threefolds in this pencil are rational. In this talk, I will give an alternative prove of both these results. To do this, I will describe Q-factorizations of the double cover of the four-dimensional projective space branched over the Igusa quartic, which is known as Coble fourfold. Using this, I will show that $\mathbb{S}_6$-symmetric quartic threefolds are birational to conic bundles over quintic del Pezzo surfaces whose degeneration curves are contained in the pencil studied by Wiman and Edge.

This is a joint work with Alexander Kuznetsov and Constantin Shramov (Moscow). ]]>

Mathematical modelling of transmission dynamics of Opisthorchis viverrini]]>

Nonlocal obstacle problems: regularity of the solutions and the free boundaries

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We will introduce some recent results in collaboration with L. Caffarelli and X. Ros-Otonon the optimal regularity of the solutions and the regularity of the free boundaries (near regular points) for nonlocal obstacle problems.The main novelty is that we obtain results for different operators than the fractional Laplacian. Indeed, we can consider infinitesimal generators of non rotationally invariant stable L ́evy processes.

]]>From noncommutative motivic measures to subgroups of the Cremona group

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

I will introduce the Grothendieck ring of triangulated categories, and show how, using Bondal-Larsen-Lunts motivic measure, a subgroup of such ring will define a subgroup of the group Bir(X) of birational self-maps of X. A main example is given by the filtration via the motivic dimension, which induces a filtration on Bir(X). As a consequence, in the case X=P

Blowup for NLS]]>

Small volume asymptotics for elliptic equations and their use in impedance tomography

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Geometry of the moduli of parabolic bundles on elliptic curves

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The former moduli space is itself related to the moduli space of rank 2 parabolic bundles over a 5-punctured P

The Arrow of Time

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

recap of properties of (relative) entropy, the following examples of irreversible behavior are discussed:

(1) The second law of thermodynamics is discussed within quantum statistical mechanics.

(2) It is indicated how Brownian motion of a quantum particle immersed in a heat bath can be derived from unitary quantum dynamics of the total system.

(3) Motion with friction is discussed in an example of Hamiltonian evolution equations for a particle moving through a dispersive wave medium.

(4) It is sketched that and why quantum dynamics is fundamentally irreversible. ]]>

Curves and moduli]]>

Blowup for Fractional NLS

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In this talk, we give sufficient criteria for blowup of solutions to nonlocal Schrödinger equations with focusing power-type nonlinearity. To give an outline of the arguments used in the proof, let us mainly focus on the mass-supercritical problem posed on the whole space R^{n} with prescribed radial initial datum of negative energy.

This is a joint work with Thomas Boulenger and Enno Lenzmann

]]>Liouville type equation on R^n]]>

IGA BEM for Maxwell eigenvalue problems

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

To live up to the promises of IGA, namely closing the gap bewteen design and analysis, we suggest an IGA boundary element method (BEM). We will review the state-of-the-art of all relevant building blocks. We will address the B-spline de Rham complex on a boundary manifold, the Galerkin discretization of the electric field integral equation, and present a convergence result. We will discuss a recent contour integral method [1] to solve the resulting non-linear eigenvalue problem. Aspects of integrating so-called ”fast methods” will also be presented, in particular Adaptive Cross Approximation [5] and Calderón preconditioning [4].

[1] W.-J. Beyn. An integral method for solving nonlinear eigenvalue problems. Linear Algebra Appl, 436(10):3839–3863, 2012.

[2] A. Buffa, G. Sangalli, and R. Vázquez. Isogeometric analysis in electromagnetics: B-splines approximation. Comput Method Appl M, 199:1143–1152, 2010.

[3] J. Corno, C. de Falco, H. De Gersem, and S. Schöps. Isogeometric simulation of Lorentz detuning in superconducting accelerator cavities. Comput Phys Commun, 201:1–7, February 2016.

[4] J. Li, D. Dault, B. Liu, Y. Tong, and B. Shanker. Subdivision based isogeometric analysis technique for electric field integral equations for simply connected structures. J Comput Phys, 319:145–162, 2016.

[5] B. Marussig, J. Zechner, G. Beer, and T.-P. Fries. Fast isogeometric boundary element method based on independent field approximation. Comput Method Appl M, 284:458–488, 2015.

The work of Stefan Kurz is supported by the ’Excellence Initiative’ of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universität Darmstadt.

]]>Recent approaches to significant pattern mining in genetics]]>

Rademacher’s Theorem, Cheeger’s Conjecture and PDEs for measures

Tags: TAG Events Forschung Informatik, TAG Events DMI]]>

The classical Rademacher Theorem asserts that every Lipschitz function is differentiablea lmost everywhere with respect to Lebesgue measure. On the other hand, Preiss (’90) gave a surprising example of a nullset in the plane such that every Lipschitz function is differentiable at at least one point of this set. Thus, it is a natural question to ask whether there exists a singular measure such that all Lipschitz functions are differentiable with respect to this singular measure. It turns out that this question has an intricate connection to the geometric structure of normal one-currents. In this talk I will present a converse to Rademacher’s Theorem, which settles the question in the negative in all dimensions: if a positive measure μ has the property that all Lipschitz functions are μ-a.e. differentiable, then μ is absolutely continuous with respect to Lebesgue measure (in the plane, this question was already solved by Alberti, Csornyei and Preiss in ’05). In a geometric context, Cheeger conjectured in ’99 that in all Lipschitz differentiability spaces (which are essentially Lipschitz manifolds in which Rademacher’s Theorem holds) likewise there is a “functional converse” to Rademacher’s Theorem. As the second main result, I will present a recent solution to this conjecture.Technically, the proofs of both of these theorems are based on a recent structure result for the singular parts of PDE-constrained measures, its corollary on the structure of normalone-currents, and the powerful theory of Alberti representations.

This is a joint work with A. Marchese and G. De Philippis

]]>Towards hyperelliptic curve cryptography]]>

Betti numbers and pseudo effective cones in 2-Fano varieties

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Fractional div-curl quantities and applications to nonlocal geometric equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We investigate a fractional notion of gradient and divergence operator. We generalize the div-curl estimate by Coifman-Lions-Meyer-Semmes to fractional div-curl quantities. We demonstrate how these quantities appear naturally in nonlocal geometric equations, which can be used to obtain a regularity theory for fractional harmonic maps and critical systems with nonlocal antisymmetric potential.

This is a joint work with Armin Schikorra

]]>Optimal integration in reproducing kernel Hilbert spaces

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Uncertainty Quantification for PDEs with Anisotropic Random Diffusion]]>

Hyperbolicity of moduli spaces of abelian varieties

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Hilbert's third problem]]>

Partial Regularity for Holonomic Minimisers of Quasiconvex Functionals

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We prove partial regularity for local minimisers of certain strictly quasiconvex integral functionals, over a class of Sobolev mappings into a compact Riemannian manifold, to which such mappings are said to be holonomically constrained. Several applications to variational problems in condensed matter physics with broken symmetries will also be discussed related to the manifold constraint condition.

]]>Orthogonal tensor decomposition from an algebraic perspective

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

(Joint work with Ada Boralevi, Emil Horobet, and Elina Robeva.) ]]>

Self-organized dynamics: from emergence of consensus to social hydrodynamics

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Rationale Kurven in P^3 – Flächen und Sekanten ]]>

A Morse index formula for the Lane-Emden problem

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We consider the semilinear Lane-Emden problem (E_{p}):

-Δu = |u|^{p-1}u in B

u = 0 on ∂B

where B is the unit ball of R^{N}, N≥3, centered at the origin and 1< p < p_{S}, p_{S}=(N+2)/(N−2). We compute the Morse index of any radial solutionup of (E_{p}), for p sufficiently close to p_{S}. The proof exploits the asymptotic behavior of u_{p} as p→p_{S} and the analysis of a limit eigenvalue problem.

This is a joint work with F. De Marchis and F. Pacella

]]>Integral points on polygons and modular forms]]>

The space of Kähler metrics on singular varieties

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

This is based on a joint work with Vincent Guedj. ]]>

Reproducing kernel methods

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Furthermore, we will present a deterministic a priori (often exponential) convergence analysis via sampling inequalities which can be employed to analyze a large class of regularized reconstruction schemes.

Such an analysis enables us to derive a priori couplings of various discretization and regularization parameters. Such parameters can range from iteration numbers in numerical linear algebra, numerical evaluation of input parameters to rounding errors.

An important issue is the choice of the reproducing kernel. We will discuss some implications of such choices and address the problem of approximating the solution of a parametric partial differential equation using problem adapted kernels.

This is partly based on joint work with M. Griebel and B. Zwicknagl (both Bonn University).

]]>On projectivity of the moduli space of stable surfaces in characteristic p > 5

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Variational aspects of Liouville equations and systems on compact surfaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

A class of Liouville equations and systems on compact surfaces is considered: we focus on the Toda system which is motivated in mathematical physics by the study of models in non-abelian Chern-Simons theory and in geometry in the description of holomorphic curves in complex analysis. We discuss its variational aspects which yield existence results.

]]>Curves on a surface - How they self-intersect and why this number can be less than zero]]>

Numerical homogenization beyond periodicity and scale separation with applications to wave propagation in heterogeneous media

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

A knot theorists approach to singularities and their deformations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

About irreversibility in rarefied gas dynamics

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Quasi-Optimal Schwarz Domain Decomposition Methods for Time Harmonic Waves

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

From condensed matter physics to probability theory

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The basic laws governing atoms and electrons are well understood, but it is impossible to make predictions about the behaviour of large systems of condensed matter physics. A popular approach is to introduce simple models and to use notions of statistical mechanics. I will review quantum spin systems and their stochastic representations in terms of random permutations and random loops. I will also describe the ‘universal’ behaviour that is common to loop models in dimensions 3 and more.

]]>Mathematical Modelling of Rabies Elimination in N’Djamena, Chad]]>

An Adaptive Wavelet Method for the Solution of Boundary Integral Equations in Three Dimensions

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Groundstate solutions for a nonlinear Choquard equation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

I will discuss the existence of groundstate solutions for the Choquard equation in the whole space R^{N}. I will first consider the case of a homogeneous nonlinearity F(u) =|u|^{p}, then I will prove the existence of solutions under general hypotheses. In particular, the cases N=2 and N≥3 will have to be treated differently. The solutions are found through a variational mountain pass strategy.

Arithmetic via Hyperelliptic Curves]]>

Astronomica im Briefwechsel zwischen Leonhard Euler und Daniel Bernoulli

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Algorithmic patterns for hierarchical matrices on many-core processors

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

We are interested to use these many-core processors for the full H-matrix construction and application process. A motivation for this interest lies in the well-known claim that future standard processors will evolve towards many-core hardware, anyway. In order to be prepared for this development, we want to discuss many-core parallel formulations of classical H-matrix algorithms and adaptive cross approximations.

In the presentation, the use of H-matrices is motivated by the model application of kernel-based approximation for the solution of parametric PDEs, e.g. PDEs with stochastic coefficients. The main part of the talk will be dedicated to the challenges of H-matrix parallelizations on many-core hardware with the specific model hardware of GPUs. We propose a set of parallelization strategies which overcome most of these challenges. Benchmarks of our implementation are used to explain the effect of different parallel formulations of the algorithms.

]]>A generalization of the beer mats puzzle]]>

Expanding large global solutions of the equations of compressible fluid mechanics

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In a recent work Sideris constructed a finite-parameter family of compactly supported affine solutions to the free boundary isentropic compressible Euler equations satisfying the physical vacuum condition. The support of these solutions expands at a linear rate in time. We show that if the adiabatic exponent gamma belongs to the interval (1,5⁄3] then this moduli space of affine motions is non-linearly stable without any symmetry assumptions; small perturbations lead to global-in-time solutions that remain close to an affine motion, they are smooth in the interior of their support, and no shocks are formed in the process.Our strategy relies on two key ingredients: a new interpretation of the affine motions using an (almost) invariant action of GL(3) on the compressible Euler system and the use of Lagrangian coordinates. The former suggests a particular rescaling of time and a change of variables that elucidates a stabilisation mechanism, while the latter requires introducing new ideas with respect to the existing well-posedness theory for vacuum free boundary fluid equations.

(Joint work with Juhi Jang (USC))

]]>Functional analytic approach to dynamical systems

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In the last decade the functional analytic approach to the study of the statistical properties of dynamical systems has become very prominent. I will try to present, in their simpler form, some of the ideas involved and review some of the results.

]]>Algebraic aspects of hyperbolic volume

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The main part deals with similar features and questions about hyperbolic volume of (non-)arithmetic Coxeter orbifolds of higher dimensions. We discuss the volume problem for certain Coxeter pyramids. This family gives rise to interesting (non-)arithmetic reflection groups whose commensurability classification has recently been performed (joint work with R. Guglielmetti and M. Jacquemet).

This is a report about ongoing work. ]]>

Höhenschranken für gewisse algebraische Zahlen ]]>

Verifiable conditions for convergence rates of regularization methods for inverse problems

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Over the last years Variational Source Conditions (VSCs) have become a standard assumption for the analysis of these methods. Compared to spectral source conditions they have a number of advantages: They can be used for general nonquadratic penalty and data fidelity terms, lead to simpler proofs, are often not only sufficient, but even necessary for certain convergence rates, and they do not involve the derivative of the forward operator (and hence do not require restrictive assumptions such as a tangential cone condition). However, so far only few sufficient conditions for VSCs for specific inverse problems are known.

To overcome this drawback, we propose a general strategy for the verification of VSCs, which consists of two sufficient conditions: One of them describes the smoothness of the solution, and the other one the degree of ill-posedness of the operator. For a number of important linear inverse problems this leads to equivalent characterizations of VSCs in terms of Besov spaces and necessary and sufficient conditions for rates of convergence. We also discuss the application of our strategy to nonlinear parameter identification and inverse medium scattering problems where it provides sufficient conditions for VSCs in terms of standard function spaces.

]]>On the number of minimal models of a smooth threefold of general type

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Hilbert’s tenth problem: Diophantine equations and decidability]]>

Hierarchical Tensor Approximation

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

We propose an alternative: the Galerkin trial space is constructed using a partition of unity. By multiplying local cut-off functions with polynomials, we can obtain discretizations of arbitrary order, and local grid refinement can be realized by reducing the supports of the cut-off functions. The main challenge lies in the construction of the corresponding system matrix, since even determining the sparsity pattern involves interactions between cut-off functions on different levels of the mesh hierarchy.

Our approach leads to a sparse system matrix, the basis functions are convenient tensor products of functions on lower-dimensional domains, and local regularity can be exploited by variable-order interpolation in order to obtain close to optimal complexity.

]]>Moduli space of cubic surfaces and their anti canonical divisors

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Fractional closed geodesics and applications]]>

Tropical compactifications, Mori Dream Spaces and Minkowski bases

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

This is a work in progress with Elisa Postinghel. ]]>

Die Tate-Lichtenbaum Paarung und Supersinguläre Elliptische Kurven]]>

Towards code modernization and porting on Intel many-core architecture: the story of Gadget code

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Conjugacy classes of n-tuples in semi-simple Jordan algebras

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

The complement problem in the plane]]>

Regularization of Rational Group Actions - part 2

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Dynamics of automorphism of a particular family of affine cubic surfaces]]>

Regularization of Rational Group Actions - part 1

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

]]>

On the Wright's complex

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Uniqueness of weak solutions to transport equation with two-dimensional nearly incompressible BV vector field

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Given a bounded, autonomous vector field b: R^{2} → R^{2}, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation

(1) ∂tu + b · ∇u = 0.

We prove that uniqueness of weak solutions holds under the assumptions that b is of class BV and it is nearly incompressible. Our proof is based on a splitting technique (introduced previously by Alberti, Bianchini and Crippa) that allows to reduce (1) to a family of 1-dimensional equations which can be solved explicitly, thus yielding uniqueness for the original problem.

In order to perform this program, we use Disintegration Theorem and known results on the structure of level sets of Lipschitz maps: this is done after a suitable localization of the problem, in which we exploit also Ambrosio’s superposition principle.

This is joint work with S. Bianchini and N. A. Gusev.

]]>Parabolic equations with random coefficients on moving hypersurfaces

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

This is a joint work with Charles M. Elliott (University of Warwick, UK), Ralf Kornhuber (Free University Berlin, Germany) and Thomas Ranner (University of Leeds, UK). ]]>

Jordan groups and birational automorphisms of algebraic varieties

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Discontinuous Galerkin Method for seismic imaging in frequency domain

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Quasi-invariant gaussian measures for the 4th order NLS under sharp regularity assumptions

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Blowup Dynamics in the Keller-Segel Model of Chemotaxis

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The Keller-Segel equations model chemotaxis of bio-organisms. In a reduced form, considered in this talk, they are related to Vlasov equation for self-gravitating systems and are used in social sciences in descriptions of crime patterns. It is relatively easy to show that in the critical dimension 2 and for the mass of initial conditions greater than 8π, the solutions break down in finite time. Understanding the mechanism of this breakdown turned out to be a subtle problem defying solution for a long time. Preliminary results indicate that the solutions “blowup”. This blowup is supposed to describe the chemotactic aggregation of the organisms and understanding its universal features would allow comparison of theoretical results with experimental observations. In this talk I discuss recent results on dynamics of solutions of the (reduced) Keller-Segel equations in the critical dimension 2, which include a formal derivation and partial rigorous results on the blowup dynamics of solutions.

(The talk is based on joint work with S. I. Dejak, D. Egli and P.M. Lushnikov.)

]]>Robust Coarse Space Construction for Domain Decomposition Methods

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

The existence of morphisms from a Calabi-Yau manifold

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

p-adic numbers and their interplay with complex geometry]]>

BMO, quasiconformal maps, and transport equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We will explain two results about (linear and nonlinear) transport equations, quasiconformal maps, and vector fields with unbounded divergence. Originally, these results are motivated by a difficult problem on Muckenhoupt weights and elliptic PDE. However, classical harmonic analysis tools allow to reformulate this problem in variational BMO terms, and then a theorem by H. M. Reimann brings naturally the connection to the transport theory.

]]>Stability and Regularity Properties of the Navier-Stokes Equation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We will discuss some regularity properties of weak solutions to the three-dimensional Navier–Stokes equation. We will first recall the classical partial regularity theory, developed by Scheffer and later by Caffarelli–Kohn–Nirenberg. Then we will present some new results in both the small data and perturbative frameworks.

]]>Model-aware Newton-solver for electrical impedance tomography

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Isomonodromic deformations of the five punctured sphere arising from complex plane quintics

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Logarithmic flat connections and monodromy]]>

Eulerian and Lagrangian continuous solutions to a non-convex balance law

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We consider continuous solutions to the single balance law ∂_{t}u+∂_{x}(f(u)) = g, g bounded, f ∈ C^{2}. We discuss correspondences among the source terms in the Eulerian and Lagrangian settings, extending previous works relative to the flux f(u) = u^{2} when possible. Counterexamples point out a new behavior of solutions when f is non-convex, and when the set of inflection points of f is not negligible, stressing the difference among the Lagrangian/Eulerian formulations in this context.

This is a joint work with G. Alberti and S. Bianchini.

]]>Scalar conservation laws with discontinuous flux

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In order to obtain uniqueness for solutions of scalar conservation laws with discontinuous flux, Kruzhkov’s entropy conditions are not enough and additional dissipation conditions have to be imposed on the discontinuity set of the flux. Understanding these conditions requires to study the structure of solutions on the discontinuity set. I will show that under quite general assumptions on the flux, solutions admit traces on the discontinuity set of the flux. This allows to show that any pair of solutions satises a Kato type inequality with an explicit reminder term concentrated on the discontinuities of the flux. Applications to uniqueness is then discussed.

]]>Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Moduli spaces and enumerative geometry]]>

On a classical question about Chern numbers

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Adaptive evolution and concentrations in parabolic PDEs

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

PSL(2,C), the exponential and some new free groups

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Modular forms and their applications]]>

Torus equivariant K-stability

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

On the concentration of entropy dissipation for scalar conservation laws

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

After a brief overview about the classical well-posedness result for scalar conservation laws, we investigate the structure of bounded solutions. In particular we prove that the entropy dissipation measure is concentrated on a countably 1-rectifiable set. In order to prove this result we introduce the notion of Lagrangian representation of the solution.

This is a joint work with Stefano Bianchini.

]]>A^1-contractibility of Koras-Russell threefolds

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Automorphism groups of affine algebraic surfaces preserving an A1-fibration

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In particular, we derive an example of a surface with infinite discrete automorphism group. ]]>

On linear inviscid damping, boundary effects and blow-up

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The Euler equations of fluid dynamics are time-reversible equations and possess many conserved quantities, including the kinetic energy and entropy. Furthermore, as shown by Arnold, they even have the structure of an infinite-dimensional Hamiltonian system. Despite these facts, in experiments one observes a damping phenomenon for small velocity perturbations to monotone shear flows, where the perturbations decay with algebraic rates. In this talk, I discuss the underlying phase-mixing mechanism of linear inviscid damping, its mathematical challenges and how to establish decay with optimal rates for a general class of monotone shear flows. Here, a particular focus will be on the setting of a channel with impermeable walls, where boundary effects asymptotically result in the formation of singularities.

]]>Automorphism groups of positive entropy of normal projective varieties

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

“Breaking Bad with Nonlocality“ & “Private Index Lookup – fetching data without revealing what is retrieved”

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Finite Element Methods in piecewise smooth domains]]>

A new approach to the classification of singular Fano-Mori 3-folds.

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Additive group actions on algebraic varieties

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In this talk we present some recent results about additive group actions on non-necessarily affine algebraic varieties that generalize the usual description of additive group actions on affine varieties via locally nilpotent derivations. In particular, we provide a characterization of additive group actions on a wide class of algebraic varieties in terms of a certain type of integrable vector fields. ]]>

Möbius invariant versions of the Willmore flow and related evolution equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

While the Willmore energy is invariant under Möbius transformations, its negative L^{2}-gradient flow is not - simply because the L^{2}-scalar product used in its definition does not have this invariance. In this talk we present Möbius invariant versions of the Willmore flow picking up ideas of Ruben Jakob and Oded Schramm. We will discuss its uses and limitations and prove well-posedness of the Cauchy problem and attractivity of local minimizers.

Noncommutative invariant algebras and weighted homographic actions

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In the particular case of homography groups, we will give in this talk an overview of some results about this topic involving transvectants, modular forms and Rankin-Cohen brackets. ]]>

Calculating the energy of molecules. A computational introduction to chemistry and wavelet boundary element methods.]]>

Networks of curves in the plane moving by curvature

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I consider the motion by curvature of a network of curves in the Euclidean plane and I discuss existence, uniqueness, and asymptotic behavior of the evolution. In particular, I focus on two model cases: a regular embedded network composed by three curves with fixed endpoints (triod) and a regular embedded network composed by two curves, one of which is closed (spoon). After talking about the state of art of the problem, I will present some new and possibly ”incoming” results obtained with Carlo Mantegazza and Matteo Novaga.

]]>Cohomological action of automorphisms of compact Kaehler threefolds

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Groups of automorphisms of some affine varieties

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Intersection product and first Chern class]]>

On Moser type inequalities in the whole space

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The Trudinger-Moser inequality is a substitute for the well known Sobolev embedding theorem when the limiting case is considered. We discuss Moser type inequalities in the whole space which involve complete and reduced Sobolev norm.Then we investigate the optimal growth rate of the exponential type function both in the first order case and in the higher order case.

]]>Model order reduction with adaptive finite element POD and application to uncertainty quantification

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Standard techniques assume that all snapshots use one and the same spatial mesh. I present a generalization for unsteady adaptive finite elements, where the mesh can change from time step to time step and, in the case of stochastic sampling, from realization to realization. I will answer the following questions: How can the coding effort for creating such a reduced-order model be minimized? How can the union of all snapshot meshes be avoided? What is the main difference between static and adaptive snapshots in the error analysis of Galerkin reduced-order models?

As a numerical test case I consider a two-dimensional viscous Burgers equation with smooth initial data multiplied by a normally distributed random variable. The results illustrate the convergence properties with respect to the number of POD basis functions and indicate possible savings of computation time.

]]>Quadratic maps with a periodic critical point of period 2

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Holomorphic self-maps with relatively compact image]]>

The finiteness problem for minimal surfaces of bounded index in a 3-manifold

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Given a closed, Riemannian 3-manifold (N, g) without symmetries (more precisely: generic) and a non-negative integer p, can we say something about the number of minimal surfaces it contains whose Morse index is bounded by p? More realistically, can we prove that such number is necessarily finite? This is the classical ”generic finiteness” problem, which has a rich history and exhibits interesting subtleties even in its basic counterpart concerning closed geodesics on surfaces. We settle such question when g is a bumpy metric of positive scalar curvature by proving that either finiteness holds or N does contain a copy of RP^{3} in its prime decomposition and we discuss the obstructions to any further generalisation of such result. When g is assumed to be strongly bumpy (meaning that all closed, immersed minimal surfaces do not have Jacobi fields, a notion recently proved to be generic by White) then the finiteness conclusion is true for any compact 3-manifold without boundary.

Dimension-adaptive sparse grid simulations of multiscale viscoelastic flows

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Singular Moser-Trudinger inequalities and their extremals]]>

Nonlinear Bounds in Hölder Spaces for the Monge-Ampère Equation

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It is well known that for many second-order PDEs the solution v gains two derivatives with respect to the right-hand side g in Hölder spaces. Often, however, it is useful to have a quantitative understanding of regularity. In ’89, Caffarelli proved interior a priori estimates for fully nonlinear, uniformly elliptic equations. Specifically, he showed that ‖v‖_{C2,α(B_{1/2})}≤C(‖v‖_{L∞(B_{1})}+‖g‖_{Cα(B_{1})}) and C∼1/α as α→0. The natural question to ask is then: Can one extend such quantitative estimates to other equations? An equation that appears frequently in analysis, geometry, and applications is the Monge-Ampére equation det(D^{2}u) = f. The Monge-Ampère equation enjoys the same qualitative regularity gains as its linear counterpart the Poisson equation in the appropriate setting, and so we ask whether or not the quantitative picture is also the same. This is not the case. In this talk, we will first review Caffarelli’s interior a priori estimates. Then, we will move to the Monge-Ampère equation and see a different picture.

(Joint work with Alessio Figalli and Connor Mooney)

]]>Self-similar blowup in nonlinear wave equations

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Blowup via self-similar solutions is ubiquitous in nonlinear wave equations, in particular in the energy-supercritical case. There are many examples where a self-similar solution is actually conjectured to describe the generic blowup of the equation. I will report on recent progress in understanding the stability of self-similar solutions in semilinear wave equations.

]]>On electrorheological fluids

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We discuss the existence theory for different models describing the motion of electrorheological fluids.

]]>Intrinsic Finite Element Methods

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Heights and elliptic curves]]>

Regularity issues for some nonlocal and nonlinear elliptic equations

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In this talk, I will review some regularity results for weak solutions of nonlocal variants of the p-Laplace equation. The model case is given by the Euler-Lagrange equation of an Aronszajn–Gagliardo–Slobodeckij seminorm. In particular, I will present a higher differentiability result for solutions, recently obtained in collaboration with Erik Lindgren (KTH). I will also discuss some connections of these equations to an Optimal Transport problem with congestion effects.

]]>Separating invariants and local cohomology

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

(Joint with Jack Jeffries) ]]>

Lipschitz extensions of maps between metric spaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

A pair of metric spaces (X;Y) is said to have the Lipschitz extension property if any Lipschitz map from a subset of X into Y can be extended to a globally defined Lipschitz map to the whole space X. In this talk I will first recall some classical extension results for spaces with a linear structure, and I will present recent results for the case when the target space Y is the Heisenberg group.

]]>Controllability method for time-harmonic wave equations

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

Universal Groebner bases and Cartwright-Sturmfels ideals

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These ideas will then be applied to the study of universal Groebner bases of ideals of minors, which admit such a grading. The main tools and concepts are Z^{m} gradings, multigraded Hilbert series, universal Groebner bases, initial and generic initial ideals. I will introduce and study two families of multigraded ideals with the property that any two ideals in the same family that have the same Hilbert series also have the same generic initial ideal. I will show that ideals of minors belong to one of these families, and derive some result about their universal Groebner bases.

Combination of discretization and modelling error estimates]]>

Local eigenvalue statistics for random regular graphs

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I discuss results on local eigenvalue statistics for random regular graphs. Under mild growth assumptions on the degree, we prove that the local semicircle law holds at the optimal scale, and that the bulk eigenvalue statistics coincide with those of the GOE from random matrix theory.

(Joint work with R. Bauerschmidt, J. Huang and H.-T. Yau.)

]]>Invariance of Plurigenera for foliations on surfaces

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Purcell swimmer and sub-Riemannian geometry]]>

Effective bounds on positive characteristic singular surfaces

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Modular Forms in Number Theory and Combinatorics]]>

Crystallographic Applications of Uniform Distribution Theory

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Real algebraic surfaces with many handles in (CP^1)^3

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Multiplicative and modular diophantine problems

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Area formula for Hyperbolic Triangles and Lexell problem]]>

Invariant manifolds for the porous medium equation

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

We investigate the speed of convergence and higher-order asymptotics of solutions to the porous medium equation. Applying a nonlinear change of variables, we rewrite the equation as a diffusion on a fixed domain with quadratic nonlinearity.The degeneracy is cured by viewing the dynamics on a hypocycloidic manifold. It is in this framework that we can prove a differentiable dependency of solutions on the initial data, and thus, dynamical systems methods are applicable. Our main result is the construction of invariant manifolds in the phase space of solutions which are tangent at the origin to the eigenspaces of the linearized equation. We show how these invariant manifolds can be used to extract information on higher-order long-time asymptotic expansions.

]]>Multilevel Monte Carlo methods for multiscale problems

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

In this talk, I will give an introduction to multilevel Monte Carlo methods in the case when the variance of the detail does not converge uniformly. The idea is illustrated by the calculation of the expectation for an elliptic problem with a random multiscale coefficient and then extended to approximations of statistical solutions to the Navier-Stokes equations.

]]>Some properties of the group GL_2(C[X_1, . . . , X_m]) and some applications to the polynomial automorphism group Aut(A^n) of the affine space A^n

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Multiplication polynomials and relative Manin-Mumford

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

0→**G**_{a} →G→E→0

where Ga is the additive group. The famous Manin-Mumford conjecture, proved by Hindry for such G, states that the intersection of a curve in G with its set of torsion points is finite unless the curve is contained in an algebraic subgroup. We will present a relative version of this theorem for families of additive extensions. Afterwards we will discuss some consequences of this result for classical problems such as Pell’s equation in polynomials and elementary integration.

]]>Calculating Gauss norms in polynomial continued fractions]]>

Barycenter technique and two remaining questions in Geometric Analysis

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

In this talk, we will present our recent solutions of the remaining cases of the boundary Yamabe problem and the Riemann mapping problem asked by Escobarin 1992. Rather than discussing our arguments of proofs, we will focus more on explaining the barycenter technique of Bahri-Coron which we employ. We hope by doing this to allow an easier understanding for the audience, since it seems to us, that even among experts, the barycenter technique is not known like the minimizing technique of Aubin-Schoen. Moreover, we hope also the audience to see how naturally the barycenter technique fits into conformally invariant variational problems verifying the structure of quantization and strong interaction phenomena.

(Joint work with M. Mayer of University of Giessen)

]]>On the fibres of Mori fibre spaces

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Persistent Homology]]>

Adams inequality on the Hyperbolic space

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In this talk we will discuss the classical Adams inequality and its versions in the hyperbolic space. We will also discuss the hyperbolic versions of Adachi-Tanaka type inequalities and the exact growth.

]]>Conforming Approximations of Bingham Type Fluid Flows

Tags: TAG Events DMI, TAG Events Forschung Mathematik]]>

In the general context of a convex lower semi-continuous functional on a Hilbert space, we prove the convergence of time implicit space conforming approximations, without viscosity and for non-smooth data. Then we introduce a general class of total variation functionals, for which we can apply the regularization method. We consider the time implicit regularized, linearized or not, algorithms, and prove their convergence for general total variation functionals.

]]>A symplectic version of the Chevalley restriction theorem for polar representations

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

Flows of singular vector fields and applications to fluid and kinetic equations

Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

Distinguishing Knots]]>

On compactness of solution of the Quantum Navier-Stokes equations

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In this talk we focus on a new compactness result about weak solutions of the quantum Navier-Stokes equations. The novelty of the result is that we are able to consider the vacuum in the definition of weak solutions. The main tool is a new formulation of the equations which allows us to get an additional a priori estimate to prove compactness. Some remarks concerning the choice of the approximation system to get global existence will be made.

(Joint work with Paolo Antonelli)

]]>Family of exotic affine spheres

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On Bressan's Mixing Conjecture and Related Results]]>

Monte Carlo Methods and Mean Field Approximation for Stochastic Particle Systems

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In 2012, my Master thesis developed different versions of Multilevel Monte Carlo (MLMC) for particle systems, both with respect to time steps and number of particles and proposed using particle antithetic estimators for MLMC. In that thesis, I showed moderate savings of MLMC compared to Monte Carlo. In this talk, I recall and expand on these results, emphasizing the importance of antithetic estimators in stochastic particle systems. I will finally conclude by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.

]]>Tags: TAG Events Forschung Mathematik, TAG Events DMI, TAG Events Perlenkolloquium]]>

High-Order Accurate Energy-Stable Finite Difference Methods]]>

On the geometry of matrix multiplication

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Schwarz Methods as Preconditioners for Non-linear Problems

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On Cremona Representations

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In this talk I will recall some properties of Cr

Local Exponential Runge-Kutta Methods]]>

Compactness and stability issues for Einstein-Lichnerowicz constraints system

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I will survey recent results on the Einstein-Lichnerowicz constraints system which appears in general relativity when trying to formulate the Cauchy problem for the Einstein equation coupled with a scalar field. I will discuss existence, uniqueness,compactness and stability for this system. This is a joint work with Bruno Premoselli.

]]>What is the (fractional) Laplacian?

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No previous expertise on the subject is needed.

]]>Numerical modeling of light interaction with matter on the nanoscale using DGTD methods

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This is a joint work with Claire Scheid and Jonathan Viquerat.

[1] Fezoui, L., S. Lanteri, S. Lohrengel, and S. Piperno. Convergenceand stability of a discontinuous Galerkin time-domain method for the3D heterogeneous Maxwell equations on unstructured meshes. ESAIM:Math. Model. Numer. Anal., Vol. 39, No. 6, 1149-1176, 2005.

]]>Birational equivalence of divisors and T-varieties

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Efficient Explicit Time Integration for the Simulation of Acoustic and Electromagnetic Waves

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Geschichte der Mathematik früher und heute am Beispiel einer Antrittsrede von Johann I Bernoulli (1667-1748)]]>

Geometry in the Euler equations of hydrodynamics: h-principle and convex integration

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The following dichotomy between rigidity and flexibility is now well known in geometry: while uniqueness holds for smooth solutions to the isometric embedding problem, the set of solutions becomes unimaginably large if one allows rough ones. What is surprising is that this dichotomy holds for problems coming from mathematical physics,and in particular the Euler equations of fluid dynamics. In this (mainly expository) talk I will explain the h-principle and the method of convex integration. Convex geometry is the heart of the matter and profuse figures will attempt to illustrate the difficulties and how to tame them.

]]>Compactness Properties for Singular Liouville Equations and Systems

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I will give a brief overview of the main results concerning topological methods for singular Liouville equations on compact surfaces, and I will show how to extend some of them to special elliptic systems. My analysis will focus on sharp forms of the Moser-Trudinger inequality and on mass-quantization results for the SU(3) Toda System.

]]>Analytical and Numerical Homogenization of Maxwell's Equations

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This is a joint work with Sonia Fliss and Patrick Ciarlet.

]]>Efficient Explicit Time Integration for the Simulation of Acoustic and Electromagnetic Waves]]>

Optimal trace ideals properties of the Fourier restriction operator and applications

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We study the trace ideals properties of the Fourier restriction operator to hypersurfaces. Equivalently, we generalize the theorems of Stein-Tomas and Strichartz to systems of orthonormal functions, with an optimal dependence on the number of such functions. As an application, we deduce new Strichartz inequalities describing the dispersive behaviour of the free evolution of quantum systems with an infinite number of particles. This is a joint work with Rupert Frank.

]]>Some recent results on the Jacobian equation

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Given two functions f and g,we want to find a map φ such that

g(φ(x)) det∇φ(x)=f(x) x∈Ω,

φ(x)=x x∈∂Ω.

Local case. We first consider the (local) existence, uniqueness and optimal regularity for the problem

g_{i}(φ(x)) det∇φ(x)=f_{i}(x) for every 1≤i≤n

where g_{i}·f_{i}>0.

*Global case*. A necessary condition is then

∫_{Ω} f =∫_{Ω} g. (1)

(i) We discuss the case where g·f>0 and give three different ideas for the existence problem with optimal regularity.

(ii) We then briefly comment on the case where g>0 but f is allowed to change sign.

*A problem without the condition (1)*. We consider a more general problem of the form

det∇φ(x)=f(x,φ(x),∇φ(x)) x∈Ω,

φ(x)=x x∈∂Ω.

where no constraint of the type (1) is needed.

]]>

Recent progresses in nonlinear potential theory

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Passages through resonances and capture into resonance in dynamics of charged particles

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A fully discrete approximation of the one-dimensional stochastic wave equation

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This is a joint work with Lluís Quer-Sardanyons, Universitat Autònoma de Barcelona.

]]>Special reductive groups over an arbitrary field

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Topology of real algebraic curves in the projective plane]]>

A counter-example concerning regularity properties for systems of conservation laws

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In 1973 Schaeffer established a result that applies to scalar conservation laws with convex fluxes and can be loosely speaking formulated as follows: for a generic smooth initial datum, the admissible solution is smooth outside a locally finite number of curves in the (t,x) plane. Here the term ”generic” should be interpreted in a suitable technical sense, related to the Baire Category Theorem. My talk will aim at discussing a recent explicit counter-example that shows that Schaeffer’s Theorem does not extend to systems of conservation laws. The talk will be based on joint works with Laura Caravenna.

]]>Adaptive inversion methods for the Helmholtz equation]]>

Results and conjectures about some isoperimetric problems with density

Tags: TAG Events Forschung Mathematik, TAG Events DMI]]>

The standard isoperimetric inequality states that among all sets with a given fixed volume(or area in dimension 2) the ball has the smallest perimeter. That is, written here for simplicity in dimension 2, the following infimum is attained by the ball

2πR= inf{∫_{∂Ω} 1 dσ(x) : Ω⊂**R**^{2} and ∫_{Ω} 1 dx=πR^{2}}.

The isoperimetric problem with density is a generalization of this question: given two positive functions f,g:**R**^{2}→**R**^{2} one studies the existence of minimizers of

I(C) = inf{∫_{∂Ω} g(x) dσ(x) : Ω⊂**R**^{2} and ∫_{Ω} f(x) dx=C}.

I will mainly talk about the situation when f(x) =|x|q and g(x) =|x|p.This is a reach problem with strong variations in difficulties depending on the values of p and q. Some cases are still an open problem. One case has an interesting application related to the Moser-Trudinger imbedding. I will also mention the situation when f=g=eψ is strictly positive and radial, which leads to the log-convex density conjecture.

]]>Affine n-Space is Characterized by its Automorphisms

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We also show that every torus appears as Aut(X) for a suitable affine variety X, but that Aut(X) cannot be isomorphic to a semisimple group. In fact, if Aut(X) is finitedimensional and if X \not\simeq

Concerning the structure of Aut(

Finally, we prove that every non-trivial homomorphism φ: SAut(

Numerical treatment of boundary integral equations and stochastic PDE]]>

A generalization of Gromov’s almost flat manifold theorem

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Almost flat manifolds are the solutions of bounded size perturbations of the equation Sec=0 (Sec is the sectional curvature). In a celebrated theorem, Gromov proved that the presence of an almost flat metric implies a precise topological description of the underlying manifold.

Integral pinching theorems express curvature assumptions in terms of certain L^{p}-norms and try to deduce topological conclusions. But typically one needs to require p >n2, where n is the dimension of the manifold, to prove such rigidity theorems.

During this talk we will explain how, under lower sectional curvature bounds, to imposeanL1-pinching condition on the curvature is surprisingly rigid, leading indeed to the same conclusion as in Gromov’s theorem under more relaxed curvature conditions.

This is a joint work with B. Wilking.

]]>Explicit counterexamples to the Laurent Cancellation Problem

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Segmentation and Classification of Inner Structures of the Spinal Cord on MRI Images with Continuous Graph Cuts and Principal Component Analysis]]>

One Shot Inverse Scattering and Source Splitting

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Besides standard regularization methods, which are often iterative, a completely different methodology - so-called qualitative reconstruction methods - has attracted a lot of interest recently. These algorithms recover specific qualitative properties of scattering objects or anomalies inside a medium in a reliable and fast way. They avoid the simulation of forward models and need no a priori information on physical or topological properties of the unknown objects or inhomogeneities to be reconstructed. One of the drawbacks of currently available qualitative reconstruction methods is the large amount of data required by most of these algorithms. It is usually assumed that measurement data of waves scattered by the unknown objects corresponding to infinitely many primary waves are given - at least theoretically.

We consider the inverse source problem for the Helmholtz equation as a means to provide a qualitative inversion algorithm for inverse scattering problems for acoustic or electromagnetic waves with a single excitation only. Probing an ensemble of obstacles by just one primary wave at a fixed frequency and measuring the far field of the corresponding scattered wave, the inverse scattering problem that we are interested in consists in reconstructing the support of the scatterers. To this end we rewrite the scattering problem as a source problem and apply two recently developed algorithms - the inverse Radon approximation and the convex scattering support - to recover information on the support of the corresponding source. The first method builds upon a windowed Fourier transform of the far field data followed by a filtered backprojection, and although this procedure yields a rather blurry reconstruction, it can be applied to identify the number and the positions of well separated source components. This information is then utilized to split the far field into individual far field patterns radiated by each of the well separated source components using a Galerkin scheme. Finally we compute the convex scattering supports associated to the individual source components as a reconstruction of the individual scatterers. We discuss this algorithm and present numerical results.

]]>Classical Invariant Theory and Category O

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Mapping class group and delta-hyperbolicity of the curve graph]]>

Global solutions and asymptotics of Teichmüller harmonic map flow

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Teichmüller harmonic map flow is a gradient flow of the Dirichlet energy which is designed to evolve parametrized surfaces towards critical points of the area. In this talk we will discuss the construction and some new results for this flow and show in particular that for non-positively curved targets the flow changes or decomposes arbitrary closed initial surfaces into minimal immersions (possibly with branch points) through globally defined smooth solutions.

]]>Lifting real algebraic curves to real algebraic knots

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