Department of Mathematics

Search

Zurich colloquium in mathematics

×

Modal title

Modal content

Please subscribe here if you would you like to be notified about these events via e-mail. Moreover you can also subscribe to the iCal/ics Calender.

Spring Semester 2025

Date / Time Speaker Title Location
11 March 2025
16:30-18:15 		Charles Bordenave
Université Aix Marseille
Details

Zurich Colloquium in Mathematics

Title Random perturbation of Toeplitz matrices
Speaker, Affiliation Charles Bordenave, Université Aix Marseille
Date, Time 11 March 2025, 16:30-18:15
Location KO2 F 150
Abstract Toeplitz matrices form a rich and ubiquitous class of possibly non-normal matrices. Their asymptotic spectral analysis in high dimension is well-understood, as illustrated by the strong Szegö limit theorem for Toeplitz determinants. The spectra of these matrices are notoriously highly sensitive to small perturbations. In this talk, we explore the spectrum of a banded Toeplitz matrix perturbed by a random matrix in the asymptotic of high dimension. We show that the outlier eigenvalues are driven by a low-dimensional random analytic matrix field alongside an explicit deterministic matrix that captures the algebraic structure of the resonances responsible for the outlier eigenvalues. Along the way, we present new variations around the strong Szegö limit theorem. The talk is based on a joint work with Mireille Capitaine and François Chapon.
Random perturbation of Toeplitz matricesread_more
KO2 F 150
29 April 2025
16:30-17:15 		Endre Süli
University of Oxford
Details

Zurich Colloquium in Mathematics

Title Hilbert's 19th problem and discrete De Giorgi{Nash{Moser theory: analysis and applications
Speaker, Affiliation Endre Süli, University of Oxford
Date, Time 29 April 2025, 16:30-17:15
Location KO2 F 150
Abstract Models of non-Newtonian fluids play an important role in science and engineering and their mathematical analysis and numerical approximation have been active fields of research over the past decade. This lecture is concerned with the analysis of numerical methods for the approximate solution of a system of nonlinear partial differential equations that arise in models of chemically-reacting viscous incompressible non-Newtonian fluids, such as the synovial fluid found in the cavities of synovial joints. The synovial fluid consists of an ultra-filtrate of blood plasma that contains hyaluronic acid, whose function is to reduce friction during movement. The shear-stress appearing in the model involves a power-law type nonlinearity, where the power-law exponent depends on a spatially varying nonnegative concentration function, expressing the concentration of hyaluronic acid, which, in turn, solves a nonlinear convection-diffusion equation. In order to prove convergence of the sequence of numerical approximations to a solution of this coupled system of nonlinear partial differential equations one has to derive a uniform Hölder norm bound on the sequence of approximations to the concentration in a setting where the diffusion coefficient in the convection-diffusion equation satisfied by the concentration is merely a bounded function with no additional regularity. This necessitates the development of a discrete counterpart of the De Giorgi--Nash--Moser theory, which is then used, in conjunction with various compactness techniques, to prove the convergence of the sequence of numerical approximations to a weak solution of the coupled system of nonlinear partial differential equations under consideration
Hilbert's 19th problem and discrete De Giorgi{Nash{Moser theory: analysis and applicationsread_more
KO2 F 150
20 May 2025
16:30-18:15 		Nalini Anantharaman
Université de Strasbourg
Details

Zurich Colloquium in Mathematics

Title Chaos and the spectral theory of hyperbolic surfaces
Speaker, Affiliation Nalini Anantharaman, Université de Strasbourg
Date, Time 20 May 2025, 16:30-18:15
Location KOF 2 F150
Abstract The main question in quantum chaos is to relate the chaotic properties of a dynamical system (like a billiard in a bounded domain, or the geodesic flow on a closed manifold) to the spectral properties of the corresponding Schrödinger operator in quantum mechanics (the laplacian, in the examples above). This is usually asked for a given dynamical system, but one may try to make the problem more tractable by studying a "random" billiard, or the geodesic flow on a "random manifold". Several years ago, I became interested in the ergodic and spectral properties of random hyperbolic surfaces, in the asymptotic regime where the area of the surface goes to infinity. I will survey the existing techniques and some of the results.
Chaos and the spectral theory of hyperbolic surfacesread_more
KOF 2 F150

Notes: the highlighted event marks the next occurring event.

Archive: SS 25 AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

JavaScript has been disabled in your browser