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

This PhD seminar serves as a preparation/follow up for the Oberseminar "Geometrische Analysis und Zahlentheorie" which treats research topics in analysis and number theory. The participants of this seminar are mostly PhD students, but advanced Bachelor's and Master's students are generally welcome.

The seminar's second purpose is to further the communication and exchange between the Phd students of the various subject areas located in Paderborn. Outside the regular terms the seminar provides its participants an opportunity to present their own research in an informal environment.

The seminar usually takes place Thursdays 11-12:30 am and (for now) online via Zoom. If you are interested to either participate regularly or to contribute a particular talk please contact Philipp Schütte via Email.

### Seminar Program

| Dominik Brennecken: Construction and elementary properties of p-adic numbers. |

Kaj Simon Bäuerle: Introduction to the theory of Bruhat-Tits buildings. | |

30.04.2021 | Philipp Schütte: Guillemin trace formula and meromorphic continuation of Selberg zeta functions for Anosov flows on compact Riemannian manifolds. |

06.05.2021 | Lasse Wolf: Discrete Series for $SL(2, \mathbb{R})$, Rankin-Cohen bracket and symmetry breaking operators. |

10.06.2021 | Lasse Wolf: Spectral theory of hyperbolic surfaces. |

17.06.2021 | Philipp Schütte: Shift systems and Markov shifts. |

24.06.2021 | Clemens Weiske: Metaplectic representation of $Sp(n, \mathbb{R})$. |

08.07.2021 | Dominik Brennecken: Translation operators in Dunkl theory. |

05.08.2021 | Benjamin Küster: Introduction to B-calculus and blow-ups. |

12.08.2021 | Philipp Schütte: Numerical calculation of resonances on Schottky surfaces. |

30.09.2021 | Philipp Schütte: Introduction to ergodic theory. |

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

| 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 $H_n$. | |

| Dominik Brennecken: Introduction to Dunkl theory and its connections with various areas of mathematics. |

07.01.2021 | Martin Baric: A historical introduction to elliptic curves and modular forms, together with their relationsship to number theory. |

14.01.2021 | Kaj Simon Bäuerle: L-functions of modular forms, the subconvexity problem, and automorphic forms associated with modular forms. |

21.01.2021 | Philipp Schütte: Introduction to microlocal tools and techniques in the context of partial differential operators. |

28.01.2021 | Andreas Mono: On Modular Forms and Harmonic Maass Forms - A Quick Survey. |

11.02.2021 | Dominik Brennecken: Introduction to the representation theory of compact groups. |

18.02.2021 | Christian Arends: Highest weight representations and representation theory of $SO(3)$. |

04.03.2021 | Lasse Wolf: Perturbation theory of bounded linear operators. |

11.03.2021 | Philipp Schütte: Introduction to quantum mechanics for mathematicians with special emphasize on representation theory applications. |

18.03.2021 | Christian Arends: Tensor product of representations and their decomposition. |

25.03.2021 | Kaj Simon Bäuerle: Introduction to reductive groups. |