# Oberseminar Winter 2024/25

Die Vorträge finden jeweils donnerstags um 16:45 Uhr im **Raum WSC-N-U-3.05** (im Mathematikgebäude ) statt.

Der Tee findet ab 16:15 in Raum O-3.46 statt.

Alle Interessenten sind herzlich eingeladen!

The seminar takes place on Thursday, starting at 4:45pm. The duration of each talk is about 60 minutes. Before the talk, at 4:15pm, there is tea in room O-3.46.

Everybody who’s interested is welcome to join.

Directions from the train station.

10.10.2024 | Yu Min (Imperial) | Classicality of derived Emerton—Gee stack for general groups |

31.10.2024 | Dimitri Wyss (EPFL) | Non-archimedean integration on quotients |

7.11.2024 | Pol Van Hoften (VU Amsterdam) | A new proof of the Eichler—Shimura congruence relation |

14.11.2024 | Georg Tamme (Universität Mainz) | tba |

21.11.2024 | Tasho Kaletha (Bonn) | tba |

28.11.2024 | N. N. | tba |

5.12.2024 | Alberto Merici (Universität Heidelberg) | tba |

12.12.2024 | Riccardo Zuffetti (TU Darmstadt) | tba |

19.12.2024 | N. N. | tba |

9.1.2025 | Nikolaos Tsakanikas (EPFL) | tba |

16.1.2025 | Claudius Heyer (Paderborn) | tba |

23.1.2025 | Ana Maria Botero (Bielefeld) | tba |

30.1.2025 | Benoît Cadorel (Nancy) | tba |

## Abstracts

### Yu Min: Classicality of derived Emerton—Gee stack for general groups.

Abstract: In this talk, we will define the Emerton—Gee stack for a general group scheme using the Tannakian formalism and discuss its representability. Moreover when the group scheme is a generalised reductive group as defined by Paškūnas—Quast, we will define a derived version of the Emerton—Gee stack using prismatic theory and show how it is controlled by its underlying classical stack.

### Dimitri Wyss: Non-archimedean integration on quotients.

Motivated by mirror symmerty, Batyrev defines ‘stringy’ Hodge numbers for a variety X with Gorenstein canonical singularities using motivic integration. While in general it is an open question, whether these numbers are related to a cohomology theory, the orbifold formula shows, that if X has quotient singularities, they agree with Chen-Ruan’s orbifold Hodge numbers.

I will explain how to generalize this orbifold formula to quotients of smooth varieties by linear algebraic groups. As an application we obtain identifications of stringy Hodge numbers with enumerative invariants, so-called BPS-invariants, in the case when X is the moduli space of an abelian category of homological dimension 1, for example the moduli space of semi-stable vector bundles on a curve. This is joint work with Michael Groechenig and Paul Ziegler.

### Pol van Hoften: A new proof of the Eichler—Shimura congruence relation

Abstract: Associated to a modular form f is a two-dimensional Galois representation whose Frobenius eigenvalues can be expressed in terms of the Fourier coefficients of f, using a formula known as the Eichler—Shimura congruence relation. This relation was proved by Eichler—Shimura and Deligne by analyzing the mod p (bad) reduction of the modular curve of level Γ0(p). In this talk, I will discuss joint work with Patrick Daniels, Dongryul Kim and Mingjia Zhang, where we give a new proof of this congruence relation that happens “entirely on the generic fibre” and works in great generality.