Wilhelm Killing Kolloquium: Prof. Dr. Guido Kings (Universität Regensburg): Periods and L-functions
Thursday, 02.05.2024 14:15 im Raum M4
Already Euler computed the values $\zeta(2), \zeta(4), \zeta(6),\ldots$ of the Riemann zeta function $\zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^{s}}$ to be \begin{equation*} \zeta(2k)=-\frac{(2\pi i)^{2k}}{2(2k!)}B_{2k} \end{equation*} where $B_{2k}\in \mathbb{Q}$ are the Bernoulli numbers. This formula can be seen as the easiest case of a vast conjecture by Deligne from 1977, which relates special values of $L$-functions of arithmetic varieties and their periods.
In this talk we want to give a non-technical introduction to the Deligne conjecture, aimed at general mathematical audience. In the end we discuss very recent developments, which lead to a complete proof in the case of Hecke $L$-functions.
Wilhelm Killing Kolloquium: Prof. Dr. Peter Albers (Universität Heidelberg): Symplectic billiards, a gentle introduction
Wednesday, 08.05.2024 14:15 im Raum M6
Usual (=Euclidean) billiard is physically motivated by a variational principle based on the length of cords. Replacing length by (symplectic) area leads to symplectic billiard. Through examples and pictures we will discuss first properties of and results for symplectic billiards for smooth curves as well as for polygons. Symplectic billiard has also a curious link to basic geometric approximation theory. Then we will see polygons on which symplectic billiards have surprising dynamical properties none of which are possible for Euclidean billiards. In the end I will present a theorem giving sufficient criteria for polygons to exhibit these dynamical properties. This is joint work with Sergei Tabachnikov, and Fabian Lander and Jannik Westermann.
Angelegt am Thursday, 14.03.2024 10:28 von Claudia Lückert
Geändert am Tuesday, 23.04.2024 13:41 von Claudia Lückert
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Wilhelm Killing Kolloquium: Prof. Dr. Claudia Alfes-Neumann (Universität Bielefeld): Modular forms and their generalizations in number theory and geometry
Thursday, 16.05.2024 14:15 im Raum M4
In this talk we introduce modular forms and harmonic weak Maass forms, real-analytic generalizations of holomorphic modular forms. We present applications of the theory in number theory and in the theory of elliptic curves.
Angelegt am Monday, 08.04.2024 08:19 von Claudia Lückert
Geändert am Thursday, 18.04.2024 07:22 von Claudia Lückert
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Wensing/Franzmeier: MM Spotlight on Progress reviews
Thursday, 13.06.2024 13:00 im Raum Cluster Meeting Room
MM Spotlight on Progress reviews: preparing and making use of it (MM early career researchers, especially doctoral researchers in their second and third year) offered by the MM Early Career Support
Angelegt am Thursday, 04.04.2024 10:12 von Imke Franzmeier
Geändert am Monday, 22.04.2024 07:09 von Kristina Wensing
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