Oberseminar WiSe 26/27
Die Vorträge finden donnerstags um 16:45 Uhr in Raum WSC-N-U-3.05 im Mathematikgebäude statt. Die Vorträge dauern 60 Minuten. Der Tee findet ab 16:15 Uhr in Raum O-3.46 statt. Alle Interessenten sind herzlich eingeladen!
The seminar takes place on Thursdays in Room WSC-N-U-3.05 in the Math Building , starting at 4:45pm. The duration of each talk is 60 minutes. Before the talks, there is tea in room O-3.46 at 4:15pm. Everybody who is interested is welcome to join!
Directions from the train station.
| 15.10.2026 | Julian Feuerpfeil (Milan/Besançon) | The Tame Fontaine-Mazur Conjecture, Linking Diagrams and Bockstein Spectral Sequences |
| 22.10.2026 | 14-18h Colloquium on the occasion of Georg Hein’s 60th birthday | Talks by David Ploog, Daniel Huybrechts, Klaus Altmann |
| 29.10.2026 | — | (Discussion on AI in mathematics) |
| 05.11.2026 | ||
| 12.11.2026 | Marco Seveso (Milano) | Ramanujan p-adic differential operators and p-adic integration over the Igusa towers of Siegel modular varieties. |
| 19.11.2026 | Arghya Sadhukhan (Münster) | tba |
| 26.11.2026 | ||
| 03.12.2026 | Elsa Maneval (EPFL) | |
| 10.12.2026 | ||
| 17.12.2026 | ||
| 07.01.2027 | Tamás Szamuely (Pisa) | tba |
| 14.01.2027 | Frank Neumann (Pavia) | tba |
| 21.01.2027 | ||
| 28.01.2027 | ||
| 04.02.2027 |
Abstracts
Julian Feuerpfeil: The Tame Fontaine-Mazur Conjecture, Linking Diagrams and Bockstein Spectral Sequences
The Fontaine-Mazur Conjecture predicts that certain $p$-adic Galois representations of a number field should arise from geometry. In the tame case, i.e., when the representation is only ramified at finitely many places and unramified at the $p$-adic ones, it implies that the image should be finite. In particular, if $G_{K,S}$ denotes the maximal pro-$p$ extension of a number field $K$ unramified outside a finite set $S$ of tame places, then $G_{K,S}$ should admit no nontrivial uniform quotient.
In this talk, after introducing this connection between $p$-adic Galois representations and pro-$p$ Galois groups, we develop a new approach to the latter problem using linking diagrams, Bockstein spectral sequences, and $\mathbb Z_p$-Lie algebras. Linking diagrams encode the presentations of the groups $G_{K,S}$ in a combinatorial way, while the Lie algebras serve as a linearization of potential uniform quotients. The first Bockstein differential recovers the mod-$p$ relations used in an earlier approach by J. Labute (2014), while higher Bockstein differentials yield additional congruences modulo higher powers of $p$. This allows us to remove Labute’s restriction that $p^2\nmid N(\mathfrak{q})-1$ for $\mathfrak{q}\in S$ and, together with a recent equidistribution result for linking diagrams, leads to the observation that $G_{\mathbb{Q},S}$ has no nontrivial uniform quotients with ‘‘probability’‘ at least $1-O(p^{-3})$ for $|S|=3$.
Colloquium on the occasion of Georg Hein’s 60th birthday
2:15pm. David Ploog (Univ. of Stavanger): The heart fan of an abelian category
For an abelian category we define a fan of convex cones. This is an elementary construction that I’ll explain through pictures. The concept is motivated by and related to spaces of stability conditions.
4:15pm. Daniel Huybrechts (Univ. Bonn): (Projective) bundles on (K3) surfaces
I will discuss cohomological invariants of bundles on surfaces and explain how this naturally leads to the period-index conjecture for which I will present three (or four?) approaches using a variety of different techniques.
5:30pm. Klaus Altmann (FU Berlin): A Weil decoration on $\mathbb P^4$ with 15,000 symmetries
(with Andreas Hochenegger and Frederik Witt)
For a normal algebraic variety we generalize the relation between reflexive rank one sheaves and Weil divisors to reflexive sheaves of arbitrary rank and so-called Weil decorations. The latter encodes a reflexive sheaf $F$ by a valuation $D\colon F_\eta \to {\rm Div}(X)$ on the generic stalk of $F$ over the function field $K(X)$.
As an application, we present a natural generalization of the celebrated Horrocks-Mumford bundle. Moreover, we study its well-known symmetries in terms of the defining Weil decoration.
Marco Seveso: Ramanujan p-adic differential operators and p-adic integration over the Igusa towers of Siegel modular varieties.
We explain how the classical operator 2\pi i d/dz on the space of quasi-modular forms admits an algebraic incarnation and how one can interpolate it p-adically using techniques due to Graham, Pilloni and Rodrigues Jacinto. We then explain how these operators can be used in order to show that suitable de Rham complexes associated with Siegel modular forms become acyclic when one restricts them to suitable neighbourhoods of the Igusa tower.