Oberseminar Winter 2024/25
Die Vorträge finden jeweils donnerstags um 16:45 Uhr im Raum WSCNU3.05 (im Mathematikgebäude ) statt.
Der Tee findet ab 16:15 in Raum O3.46 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 O3.46.
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)  Nonarchimedean integration on quotients 
7.11.2024  

14.11.2024  Georg Tamme (Universität Mainz)  A homotopical approach to crystalline cohomology 
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  reserved  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: Nonarchimedean 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 ChenRuan’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, socalled BPSinvariants, in the case when X is the moduli space of an abelian category of homological dimension 1, for example the moduli space of semistable 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 twodimensional 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.
Georg Tamme: A homotopical approach to crystalline cohomology
A classical idea to define a padic cohomology theory for smooth varieties X over a perfect field k of characteristic p, due to Grothendieck and MonskyWashnitzer, is to choose a lift X^ of X over the ring of Witt vectors W(k) of k (if it exists) and consider the de Rham cohomology of X^. The problem with this approach is the nonunicity of such a lift. In this talk, I will present a way to make this idea work using an explicit infinity category of W(k)algebras whose higher morphisms in some sense take care of the nonunicity mentioned above. Every smooth kalgebra has a lift to this category, unique up to coherent homotopy. One can then define its de Rham cohomology, which easily globalises to smooth, nonaffine kschemes. The cohomology obtained in this way is isomorphic to crystalline cohomology of X. I will also indicate how to use this formalism to define a category of crystals, coefficients for de Rham cohomology. This is joint work with Moritz Kerz.