Vorträge in der Woche 06.05.2024 bis 12.05.2024

Montag, 06.05.2024: What is a spectral zeta function?

Anders Karlsson

PRE-COLLOQUIUM: This will be a gentle introduction to zeta functions, which is a type of generating function. The focus will be on those coming from the spectrum of a Laplacian, in particular on graphs for which the Laplacian will be defined and explained.

Montag, 06.05.2024: Heat diffusion and connections between spectral zeta functions of graphs and spaces

Anders Karlsson

Heat kernels and spectral zeta functions are symmetric functions in the Laplace spectrum. The most classical zeta and L functions in number theory are spectral zeta functions of tori (with Dirichlet character twists). Tori can be approximated by finite torus graphs, which have spectral zeta functions in perfect analogy, by the Mellin transform of a heat kernel. Also infinite regular graphs are of interest. I will explain some relationships between these continuous and discrete zeta functions. It turns out that they have closer connections than one would perhaps think. It concerns asymptotics (as considered in statistical physics), functional equations, Riemann hypotheses, special values and their appearances in volume formulas à la Minkowski-Siegel. Based on various joint works with Chinta, Jorgenson, Smajlovic, Friedli and Pallich.

Dienstag, 07.05.2024: Linear Algebraic Groups

Clemens Nollau, Lou-Jean Cobigo-Bihavan