We consider generalized symmetric operator eigenvalue problem s with random symmetric perturbations of the operators. This implies that the eigenpairs of the eigenvalue problem are also random. We investigate s tochastic quantities of interest of eigenpairs of higher but finite multip licity and discuss why for multiplicity larger than one\, only the stochas tic quantities of interest of the eigenspaces are meaningful. To do so\, w e characterize the Fréchet derivatives of the eigenpairs with respect to the perturbation and provide a new linear characterization for eigenpairs of higher multiplicity. As a side result\, we prove local analyticity of t he eigenspaces. Based on the Fréchet derivatives of the eigenpairs we dis cuss a meaningful Monte Carlo sampling strategy for multiple eigenvalues a nd develop an uncertainty quantification perturbation approach. We present numerical examples to illustrate the theoretical results.

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

DTEND;TZID=Europe/Zurich:20241108T120000 END:VEVENT BEGIN:VEVENT UID:news1733@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20240924T152337 DTSTART;TZID=Europe/Zurich:20241112T173000 SUMMARY:Bernoulli Meets Industry: Olaf Merkert (TNG Technology Consulting G mbH) DESCRIPTION:Have you ever wondered what to do after your degree?\\r\\nWe in vite you to the new seminar “Bernoulli meets Industry”\, an evening ev ent where\\r\\nformer mathematicians talk about their current work\, follo wed by an apéro.\\r\\nflyer [t3://file?uid=3748] X-ALT-DESC:Have you ever wondered what to do after your degree?

\nWe invite you to the new seminar “Bernoulli meets Industry”\, an eveni ng event where

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

\nflyer END:VEVENT BEGIN:VEVENT UID:news1715@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20241011T114002 DTSTART;TZID=Europe/Zurich:20241113T141500 SUMMARY:Seminar Analysis and Mathematical Physics: Paolo Bonicatto (Univers ità degli Studi di Trento) DESCRIPTION: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”. I n the seminar\, we will introduce the notion of locality for general linea r (first-order) differential operators and we will discuss some sufficient and necessary conditions for locality to hold. We will present several ex amples and\, if time allows\, a complete catalogue of differential operato rs in the 2D setting. This is part of ongoing projects with G. Alberti (Pi sa) and G. Del Nin (MPI\, Leipzig). X-ALT-DESC:

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:20240919T092634 DTSTART;TZID=Europe/Zurich:20241115T110000 SUMMARY:Seminar in Numerical Analysis: Marco Picasso (EPFL) DESCRIPTION:TBA\\r\\n\\r\\nFor further information about the seminar\, plea se visit this webpage [t3://page?uid=1115]. X-ALT-DESC:TBA

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

DTEND;TZID=Europe/Zurich:20241115T120000 END:VEVENT END:VCALENDAR