BiPb Research Seminar

Classical Yang-Baxter equation  (CYBE)  plays an important role in the modern theory of classical integrable systems.

In my talk,  I am going to give a survey of main properties of solutions of CYBE and explain which algebraic, analytic and geometric structures naturally arise in its framework.

In this talk I will give a short introduction to the theory of theta functions and indefinite theta functions (mostly covering work of Vignéras and Zwegers). Moreover, I will introduce period polynomials of modular forms and their zeta polynomials and report on a connection to Ehrhart polynomials established by Ono, Rolen and Sprung.

In diesem Vortrag werde ich zuerst den Begriff einer Ruelle Resonanz als Polstelle einer meromorph fortgesetzten Resolvente einführen und den Zusammenhang zum exponentiellen Mischen der dynamischen Systeme erklären. In einem zweiten Teil des Vortrages möchte ich dann darauf eingehen, wie die selben meromorphen Resolventen genutzt werden können um dynamische Zeta Funktionen meromorph fortzusetzen.                                                                                          

15.11.2019

We are concerned with classifying the finitely generated indecomposable modules for a finite-dimensional associative algebra, or more generally a ring, or some related situation, such as objects in a derived category. There are a number of situations where classifications have been obtained in terms of so-called strings and bands. This includes string algebras, clannish algebras (introduced by the speaker in 1989), Dedekind-like rings and nodal algebras. I shall review some of this work, with examples from geometry, topology and arithmetic. In addition, I aim to describe some improvements to my earlier work on clannish algebras.                                                                                                                                                                                                     

Fabian Januszewski

Global characters were introduced by Harish-Chandra as an important tool in the study of the representation theory of real reductive groups. While they share many properties of characters of finite and compact groups, their original definition and theory is inherently analytic, despite the fact that Harish-Chandra's approach to the classification of irreducible admissible representations is essentially algebraic. In this talk, I will give a homological definition of characters in this setting which on the one hand extends to larger categories of representations than Harish-Chandra's does, and on the other hand extends to other setups where the field of complex numbers is replaced by an arbitrary field or ring. The original motivation for such a theory comes from number theory and mathematical physics, where such contexts have appeared naturally.

13.12.2019

Classical special functions such as the Gaussian hypergeometric function are known to play an important role in the analysis on symmetric spaces of rank one. There are multivariable generalizations of these functions within the rational and trigonometric Dunkl theories, which allow far-reaching generalizations of the spherical analysis on Riemannian symmetric spaces.
In this talk, we give an overview of some basic ingredients of this framework. We explain the role of differential-reflection operators (called Dunkl operators), and we address some open questions and recent developments related to the harmonic analysis associated with Dunkl operators.

Barbara Baumeister

In the talk I will introduce into the broad field of non-crossing partitions. Specially I  will focus on the dual approach to Coxeter and Artin groups and give an application to representation theory of algebras.