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Dienstag, 25.01.2022 | 14.15 Uhr - 15.45 Uhr

Oberseminar Geometrische Analysis und Zahlentheorie

25.01.2022

Anders Karlsson (University of Geneva)

Titel:

Spectral zeta functions of graphs and analytic number theory
Abstract: From the spectrum of a Laplace operator one can form a zeta function. In the case of the circle it gives Riemann’s zeta function. We study such functions for certain finite and infinite graphs. These functions  appear (incognito) in several areas of mathematics and physics. In particular we study rather precise asymptotic of discrete tori as is done in statistical physics, and recover spectral zeta functions of real tori which are of interest in number theory. As it turns out, the Riemann hypothesis is equivalent to an approximate functional equation of the spectral zeta functions of cyclic graphs (whose special values incidentally appear in the Verlinde formulas in algebraic geometry / mathematical physics). Joint work with F. Friedli, G. Chinta and J. Jorgenson.  

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