PhD Seminar associated with the Oberseminar "Geometrische Analysis und Zahlentheorie"

Lasse Wolf:

Definition and Applications of the Fell topology on the unitary dual.

Organisational meeting

22.04.2021

Dominik Brennecken:

Construction and elementary properties of p-adic numbers.

Kaj Simon Bäuerle:

Introduction to the theory of Bruhat-Tits buildings.

Philipp Schütte:

Guillemin trace formula and meromorphic continuation of Selberg zeta functions for Anosov flows on compact Riemannian manifolds.

Lasse Wolf:

Discrete Series for $SL(2, \mathbb{R})$, Rankin-Cohen bracket and symmetry breaking operators.

Lasse Wolf:

Spectral theory of hyperbolic surfaces.

Philipp Schütte:

Shift systems and Markov shifts.

Clemens Weiske:

Metaplectic representation of $Sp(n, \mathbb{R})$.

Dominik Brennecken:

Translation operators in Dunkl theory.

Benjamin Küster:

Introduction to B-calculus and blow-ups.

Philipp Schütte:

Numerical calculation of resonances on Schottky surfaces.

Philipp Schütte:

Introduction to ergodic theory.

03.12.2020

Philipp Schütte:

Introduction to the construction of resonances for Anosov flows on compact manifolds using microlocal analysis and overview over the contact flow setting.

10.12.2020

Christian Arends:

Definition and properties of principle series representations of reductive Lie groups.

Lasse Wolf:

Overview over Fourier transformations for compact and abelian (locally compact) topological groups and their relationship with the representation theory of such groups.

Julia Budde:

Introduction to the properties of the Heisenberg group $H_n$ and its Lie algebra with special emphasize on the Fourier transform for $H_n$.

17.12.2020

Dominik Brennecken:

Introduction to Dunkl theory and its connections with various areas of mathematics.

Martin Baric:

A historical introduction to elliptic curves and modular forms, together with their relationsship to number theory.

Kaj Simon Bäuerle:

L-functions of modular forms, the subconvexity problem, and automorphic forms associated with modular forms.

Philipp Schütte:

Introduction to microlocal tools and techniques in the context of partial differential operators.

Andreas Mono:

On Modular Forms and Harmonic Maass Forms - A Quick Survey.

Dominik Brennecken:

Introduction to the representation theory of compact groups.

Christian Arends:

Highest weight representations and representation theory of  $SO(3)$.

Lasse Wolf:

Perturbation theory of bounded linear operators.

Philipp Schütte:

Introduction to quantum mechanics for mathematicians with special emphasize on representation theory applications.

Christian Arends:

Tensor product of representations and their decomposition.

Kaj Simon Bäuerle:

Introduction to reductive groups.