It is well known that\, given a Sobolev function vanishing in a measurable set\, the gradient must vanish almost everywhere on that set . This property is usually called “locality of the gradient operator”. In the seminar\, we will introduce the notion of locality for general lin ear (first-order) differential operators and we will discuss some sufficie nt and necessary conditions for locality to hold. We will present several examples and\, if time allows\, a complete catalogue of differential opera tors in the 2D setting. This is part of ongoing projects with G. Alberti ( Pisa) and G. Del Nin (MPI\, Leipzig).

DTEND;TZID=Europe/Zurich:20241113T160000 END:VEVENT BEGIN:VEVENT UID:news1729@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20241106T144114 DTSTART;TZID=Europe/Zurich:20241115T110000 SUMMARY:Seminar in Numerical Analysis: Marco Picasso (EPFL) DESCRIPTION:Anisotropic adaptive meshes\, that is to say adaptive meshes wi th large aspect ratio\, are extremely efficient to approach functions havi ng boundary or internal layers\, some industrial applications will be pres ented. The theory will be justified on elliptic problems\, and on the tran sport equation when using the order two Crank-Nicolson scheme.\\r\\n\\r\\n For further information about the seminar\, please visit this webpage [t3: //page?uid=1115]. X-ALT-DESC:Anisotropic adaptive meshes\, that is to say adaptive meshes with large aspect ratio\, are extremely efficient to approach functions ha ving boundary or internal layers\, some industrial applications will be pr esented. The theory will be justified on elliptic problems\, and on the tr ansport equation when using the order two Crank-Nicolson scheme.

\n\nFor further information about the seminar\, please visit this webpage.

DTEND;TZID=Europe/Zurich:20241115T120000 END:VEVENT BEGIN:VEVENT UID:news1713@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20241112T142345 DTSTART;TZID=Europe/Zurich:20241120T141500 SUMMARY:Seminar Analysis and Mathematical Physics: Tommaso Cortopassi (Scuo la Normale Superiore di Pisa) DESCRIPTION:We introduce a new stability estimate for comparing the regular Lagrangian flow of a Sobolev vector field to a piecewise affine approxima tion generated by an explicit Euler-like method\, in the spirit of Crippa- De Lellis's estimates. We use this estimate to prove approximation results for solutions of the continuity equation\, which can be represented as th e push forward of the initial datum via the regular Lagrangian flow. We gi ve two examples: a probabilistic one using Dirac deltas to approximate the initial datum and a deterministic one using a diffuse approximation inste ad. In both cases\, we assume no regularity on the mesh partitioning the s patial domain. X-ALT-DESC:We introduce a new stability estimate for comparing the regul ar Lagrangian flow of a Sobolev vector field to a piecewise affine approxi mation generated by an explicit Euler-like method\, in the spirit of Cripp a-De Lellis's estimates. We use this estimate to prove approximation resul ts for solutions of the continuity equation\, which can be represented as the push forward of the initial datum via the regular Lagrangian flow. We give two examples: a probabilistic one using Dirac deltas to approximate t he initial datum and a deterministic one using a diffuse approximation ins tead. In both cases\, we assume no regularity on the mesh partitioning the spatial domain.

DTEND;TZID=Europe/Zurich:20241120T160000 END:VEVENT BEGIN:VEVENT UID:news1723@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20240916T114921 DTSTART;TZID=Europe/Zurich:20241121T161500 SUMMARY:Perlenkolloquium: Prof. Dr. Joachim Rosenthal (UZH) DESCRIPTION:Public key cryptography has been at the center of modern crypto graphy. It is not only used for the exchange of secret keys but also for the authentication of entities on the Internet\, for digital signatures a nd for the construction of digital currencies.\\r\\nUntil a few years ago most public key systems were based on the hardness of factoring integers o r on the hardness of the discrete logarithm problem in an elliptic curve.\ \r\\nWith the realization that a quantum computer would make many practica lly used public key cryptographic systems obsolete it became an important research topic to design public key systems which are expected to be secur e even if a powerful quantum computer would exist.\\r\\nThis new area of r esearch is called post-quantum cryptography and there has been in the last couple of years a lot of efforts to come up with new standards to be used in everyday applications.\\r\\nThe main part of the lecture will overview this recent development and will explain the underlying mathematical prob lems. X-ALT-DESC:Public key cryptography has been at the center of modern cryp tography. \; It is not only used for the exchange of secret keys but a lso for the authentication of entities on the Internet\, for digital signa tures and for the construction of digital currencies.

\nUntil a few years ago most public key systems were based on the hardness of factoring integers or on the hardness of the discrete logarithm problem in an ellipt ic curve.

\nWith the realization that a quantum computer would make many practically used public key cryptographic systems obsolete it became an important research topic to design public key systems which are expecte d to be secure even if a powerful quantum computer would exist.

\nTh is new area of research is called post-quantum cryptography and there has been in the last couple of years a lot of efforts to come up with new stan dards to be used in everyday applications.

\nThe main part of the le cture will overview this recent development and will explain the underlyin g mathematical problems.

END:VEVENT BEGIN:VEVENT UID:news1758@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20241107T104418 DTSTART;TZID=Europe/Zurich:20241122T160000 SUMMARY:BZ Seminar in Analysis: Leonid Parnovski (London) DESCRIPTION:The existence of spectral asymptotics of Laplace or Schroedinge r operators acting on Riemannian manifolds is a classical problem known fo r more than 100 years. It has ben known for a long time that obstacles to the existence of spectral asymptotic expansions are periodic and looping t rajectories of the geodesic flow. A conjecture formulated in 2016 stated t hat these trajectories are the only such obstacles. I will discuss the his tory of this problem and describe the recent progress: proving this conjec ture in special cases\, as well as constructing some counterexamples. X-ALT-DESC:The existence of spectral asymptotics of Laplace or Schroedin ger operators acting on Riemannian manifolds is a classical problem known for more than 100 years. It has ben known for a long time that obstacles t o the existence of spectral asymptotic expansions are periodic and looping trajectories of the geodesic flow. A conjecture formulated in 2016 stated that these trajectories are the only such obstacles. I will discuss the h istory of this problem and describe the recent progress: proving this conj ecture in special cases\, as well as constructing some counterexamples.

DTEND;TZID=Europe/Zurich:20241122T170000 END:VEVENT BEGIN:VEVENT UID:news1759@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20241107T104835 DTSTART;TZID=Europe/Zurich:20241122T173000 SUMMARY:BZ Seminar in Analysis: David Gérard-Varet (Paris) DESCRIPTION:A popular model for suspensions of non-spherical particles in fluids is the so-called Doi model\, which couples a Stokes equation for t he fluid velocity u(t\,x) together with a transport equation for the distr ibution of particles in space and orientation f(t\,x\,p). The Doi model comes from a formal mean-field limit of a system of particles interacting inside a Stokes flow. We will show in this talk that this formal limit is not accurate and will rigorously derive a correction to the model\, under natural assumptions on the initial distribution of the particles. This is joint work with R. Höfer (Regensburg university). X-ALT-DESC:A \;popular model for suspensions of non-spherical parti cles in fluids is the so-called Doi model\, which couples a Stokes equatio n for the fluid velocity u(t\,x) together with a transport equation for th e distribution of particles \;in space and orientation f(t\,x\,p). Th e Doi model comes from a formal mean-field limit of a system of particles interacting inside a Stokes flow. We will show in this talk that this form al limit is not accurate and will rigorously derive a correction to the mo del\, under natural assumptions on the initial distribution of the particl es. This is joint work with R. Höfer (Regensburg university).

DTEND;TZID=Europe/Zurich:20241122T183000 END:VEVENT END:VCALENDAR