Oberseminar Sommersemester 2026

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.

16.04.2026	Marta Pieropan (Utrecht)	Campana points and firmaments
23.04.2026	(reserved)	t.b.a.
30.04.2026	Jelena Ivancic (MPI Bonn)	Infinitesimal characters for the completed cohomology for $\mathrm{GL}_n$ over CM fields
07.05.2026	Luca Francone (Rome)	From reductive groups to quantum groups
21.05.2026	Frank Gounelas (Bonn)	Universal Brauer-Severi Varieties
28.05.2026	Nicolas Dupré (Wuppertal)	Pro-$p$ Iwahori—Hecke modules and singularity categories
11.06.2026	Ben Moonen (Nijmegen)	Bézout’s theorem for abelian varieties.
25.06.2026	Baptiste Calmès (Lens)	Hermitian K-theory invariant by idempotent completion
02.07.2026	Joshua Jackson (Cambridge)	Towards a Harder-Narasimhan theory classifying singular curves
09.07.2026	Aryaman Patel (Saarbrücken)	The Hitchin morphism over higher-dimensional base manifolds
16.07.2026	Gabriele Bogo (Bielefeld)	Curves in Hilbert modular varieties
23.07.2026	Dario Weissmann (Madrid)	t.b.a.

Abstracts

Marta Pieropan: Campana points and firmaments

Determining the image of the set of rational points under a morphism of varieties is a very natural and difficult question. The case where the morphism is geometrically surjective has been studied extensively. From Campana’s theory of orbifolds, it follows that over a number field, the image of the set of rational points is contained in the set of Campana points for the orbifold base of the morphism. This first approximation of the image of the set of rational points is refined by Abramovich’s theory of firmaments. This talk presents some arithmetic questions about Campana points, and a proof of a claim by Abramovich about lifting firm points under toroidal morphisms in joint work with Herr, Mehidi and Poiret.

Jelena Ivancic: Infinitesimal characters for the completed cohomology for $\mathrm{GL}_n$ over CM fields

I will talk about joint work with Vaughan McDonald where we prove a conjecture of Dospinescu-Paskunas-Schraen for the case of $\mathrm{GL}_n$ over CM fields (under some assumptions). This conjecture is a part of the expected local-global compatibility at p in Langlands program: it says that the infinitesimal action on a Hecke eigenspace appearing in the locally analytic vectors of completed cohomology is given by a character which ‘‘encodes’‘ the Hodge-Tate weights of the associated Galois representation.
I will discuss this statement and our proof for $\mathrm{GL}_n$ over CM field.

Luca Francone: From reductive groups to quantum groups

In this talk, we introduce the discrete gauge action: a generalization of the conjugation action of a complex reductive algebraic group, together with a family of geometric objects called schemes of bands. We explain how these constructions provide a geometric interpretation of some fundamental objects in the representation theory of quantum affine algebras and prove a conjecture of Frenkel and Reshetikhin of 1998. This is joint work with Bernard Leclerc.

Frank Gounelas: Universal Brauer-Severi Varieties

In this talk I will define a Brauer-Severi variety $Q\to B$ which is universal in the sense that every other one with related invariants is a pullback of $Q$. The geometry of these varieties $B$ will be discussed as well as some applications to period-index problems. This is joint work with Daniel Huybrechts.

Nicolas Dupré: Pro-$p$ Iwahori—Hecke modules and singularity categories

Let $G$ be the group of rational points of a split reductive group over a nonarchimedean local field $F$ of residue characteristic $p$, and let $H$ be the associated pro-p Iwahori—Hecke algebra over a field $k$ of characteristic $p$. The mod-$p$ Langlands program aims to relate the representation theory of $G$ over $k$ to that of the absolute Galois group of $F$. The representations of $G$ in this context are however still very poorly understood. On the other hand, the $H$-modules are much better understood and there even are results relating them to Galois representations. In earlier work, we investigated the so-called Gorenstein projective model structure on the category of $H$-modules and its associated homotopy category $Ho(H)$. Assuming $G$ has semisimple rank $1$, we will explain in this talk how this category $Ho(H)$ identifies with the singularity category of a suitable scheme parametrising Galois representations. This scheme appeared previously in work of Dotto—Emerton—Gee and of Pépin—Schmidt. After taking a suitable notion of support, this recovers most of the (simple) mod-p Langlands correspondence for $\mathrm{GL}_2(\mathbb{Q}_p)$.

Ben Moonen: Bézout’s theorem for abelian varieties.

I’ll report on joint work with Olivier Debarre. The main result is that if $A$ is an absolutely simple abelian variety over some field and $X_1,…, X_r$ are subvarieties of $A$, then the dimension of their sum $X_1 + … + X_r$ equals the minimum of $dim(A)$ and $\sum dim(X_i)$. In characteristic $0$, there is a simple geometric proof for this, but that argument breaks down in characteristic $p$. Instead, we prove this result as a consequence of a theorem on perverse sheaves, building upon work of Krämer and Weissauer.

Baptiste Calmès: Hermitian K-theory invariant by idempotent completion

I’ll report on joint work with Dotto, Harpaz, Hebestreit, Land, Moi, Nardin, Nikolaus and Steimle on the Hermitian analogue of Bass K-theory, in the context of stable infinity-categories. I’ll explain how this analogue is obtained from the previously constructed Hermitian K-theory functor by further imposing idempotent completion invariance, and I’ll discuss structural properties it enjoys, such as a circle decomposition theorem.

Josh Jackson: Towards a Harder-Narasimhan theory classifying singular curves

In the Geometric Invariant Theory construction of the moduli space of semistable sheaves, one has a priori two measures of the failure of a sheaf to be semistable. The first, Harder-Narasimhan type, is sheaf-theoretic, while the second, the Hesselink-Kempf-Kirwan-Ness stratification, comes purely from GIT. Naturally enough, as proved by Hoskins, these two notions coincide in an appropriate ‘asymptotic’ sense, a fact that has recently been applied to construct moduli of unstable sheaves using new techniques from Non-reductive GIT.

This motivates the analogous questions for another major GIT success story: the moduli of curves. Namely, does there exist some asymptotic HKKN stratification in the GIT construction of the moduli space of stable curves? If so, what meaning does it have, and can it be used to construct new moduli spaces classifying singular curves?

After explaining the necessary background, I will report on joint work with Dave Swinarski towards answering the first of these questions in the affirmative, using techniques from convex optimisation.

Aryaman Patel: The Hitchin morphism over higher-dimensional base manifolds

The Hitchin morphism is a useful tool to study moduli spaces of Higgs bundles on curves. On a higher dimensional variety, however, little is known about the Hitchin morphism. I will talk about a recent work joint with Dario Weissmann, where we address a conjecture by Chen and Ngo about the image of the Hitchin morphism from the moduli stack of Higgs bundles. We show that a stronger version of the conjecture holds for a large class of varieties which includes varieties with numerically trivial canonical divisor.

Gabriele Bogo: Curves in Hilbert modular varieties

I will discuss examples of non-arithmetic curves in Hilbert modular varieties and explain how their associated Picard-Fuchs differential equations can be used to construct lifts of partial Hasse invariants for these curves. As an application, I will describe the non-ordinary locus of these curves in terms of zeros of orthogonal polynomials, extending a classical result of Kaneko and Zagier. This is partly based on joint work with Yingkun Li.