Abstract: Beilinson-Bernstein localisation provides a bridge between representations of complex semisimple Lie algebras and D-modules on the flag variety. This bridge allows one to employ geometric techniques to answer representation-theoretic questions. In this talk, I will discuss how Beilinson-Bernstein localisation can be used to study representations of real reductive Lie groups. To illustrate the concreteness of the theory, I'll start by…
Title: Teichmüller curves as the vanishing locus of modular forms
Abstract: Teichmüller curves are totally geodesic curves $C \subset \mathcal{M}_g$ inside the moduli space of curves with respect to the Teichmüller metric. We will focus on a special class of Teichmüller curves arising from Hecke triangle groups and embed them into the locus of real multiplication inside $\mathcal{A}_g$, the…
Abstract: "Dunkl operators" associated to a finite real reflection group constitute a commutative parameter family of deformations of the directional derivatives in Euclidean space. These operators are "differential-reflection" operators. Heckman and Cherednik have defined trigonometric versions of Dunkl's operators. The interest for these operators lies in their deep ties to Macdonald theory, representation theory and integrable system.
In…
Abstract: tba
Bei Interesse an einer online-Teilnahme (sei es regelmäßig oder auch nur an einem bestimmten Vortrag) bitten wir vorab mit Tobias Weich Kontakt aufzunehmen, damit der Teilnahmelink geteilt werden kann.
Title: Cospectrality of random graphs and arithmetic statistics
Abstract: A classical question in spectral graph theory asks which graphs are determined up to isomorphism by the spectrum of their adjacency matrix. Both positive and negative examples are known. But, what happens in the "typical case" of a random graph?
Haemers' conjecture posits that the probability that the graph is determined by its spectrum should tend to one as the number…
Abstract: tba
Bei Interesse an einer online-Teilnahme (sei es regelmäßig oder auch nur an einem bestimmten Vortrag) bitten wir vorab mit Tobias Weich Kontakt aufzunehmen, damit der Teilnahmelink geteilt werden kann.
