Noether-Lefschetz loci in A_g and modularity
2026-01-19 15:15 - 17:45 (Europe/Berlin) | Darmstadt
16:45 – 17:45 Johannes Horn (Goethe Universität Frankfurt): Tautological projections
16:45 – 17:45 Martin Möller (Goethe Universität Frankfurt): Modularity conjecture and Hecke orbits

Tame Local Langlands
2026-01-20 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 11: Duality on the local Langlands category
Ian Gleason (National University of Singapore)
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

Sums of Hecke eigenvalues along polynomials and arithmetic applications
2026-01-20 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Katy Woo (Stanford University): Sums of Hecke eigenvalues along polynomials and arithmetic applications
We study sums of absolute values of Hecke eigenvalues of GL(2) representations that are tempered at all finite places. We show that these sums exhibit logarithmic savings over the trivial bound if and only if the representation is cuspidal. Further, we connect the problem of studying the sums of Hecke eigenvalues along polynomial values to the base change problem for GL(2). Finally, we will describe some arithmetic applications of bounds on these sums for counting rational points on del Pezzo surfaces.
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits)

Seminar on Arithmetic Geometry
2026-01-23 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Luca Marannino (Jussieu), On anticyclotomic twists of modular forms at inert primes
In this talk, we outline an approach to the study of anticyclotomic twists of modular forms, when the fixed prime p is inert in the relevant quadratic imaginary field. After revisiting old (and less old) results involving Heegner points/cycles, we will focus on our recent work. Following ideas of Castella-Do for the “p split” case, one can envisage a construction of an anticyclotomic Euler system arising from a suitable manipulation of diagonal classes on a triple product of modular curves and obtain new p-adic evidence for the Bloch-Kato conjecture in rank 1 situations.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

Riemann-Hilbert correspondence in characteristic p
2026-01-26 10:00 - 12:00 | Mainz, Hilbertraum (05-432)
Anton Engelmann (JGU Mainz)
Unit Frobenius modules

p-adic Simpson correspondence
2026-01-27 11:00 - 16:00 | Hannover, Im Welfenschloss, Raum A412
Talk 9: Margherita Recchia (Leibniz Universität Hannover): Reduction of structure group and rigidification
Talk 10: Ronald Solodov (Leibniz Universität Hannover): Invertible ℬ-modules via the exponential

Tame Local Langlands
2026-01-27 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 12: The stack of local Langlands parameters
Zhen Huang (University of Padova)
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

On the global Gan-Gross-Prasad conjecture for GSpin groups
2026-01-27 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Pan Yan ( University of Arizona): On the global Gan-Gross-Prasad conjecture for GSpin groups
We prove one direction of the global Gan-Gross-Prasad conjecture for generic representations of GSpin groups, namely the implication from the non-vanishing of the Bessel period to the non-vanishing of the central value of L-function. The proof is based on a new Rankin-Selberg integral for GSpin groups using Bessel models.
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits)

The Bloch conductor formula
2026-01-30 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Dr. Massimo Pippi (Université Angers)
Let X be a regular scheme over the spectrum of a DVR S. Bloch conjectured a formula which relates the algebraic differential forms of X with the total dimension of the vanishing cohomology of X/S. In this talk I’ll describe a proof of this formula using methods from non-commutative and derived algebraic geometry. This is a joint work with Dario Beraldo.

Seminar on Arithmetic Geometry
2026-01-30 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Maxime Ramzi (Universität Münster): On free rigid commutative algebras
Efimov’s recent discovery of continuous K-theory has sparked some interest in the notion of dualizable categories and related objects, such as rigid commutative algebras, which appear in very varied contexts, from sheaf theory to analytic geometry. In this context, a thorough analysis of rigid commutative algebras seems to be needed.
In this talk, after giving an introduction to the context above,, I will discuss a formula for free rigid commutative algebras in the context of 2-presentably symmetric monoidal 2-categories. The formula recovers some results of Barkan and Steinebrunner, but it has some surprising features which have some consequences for the theory of rigidification of locally rigid commutative algebras, which, time permitting, I will sketch.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

Riemann-Hilbert correspondence in characteristic p
2026-02-02 10:00 - 12:00 | Mainz, Hilbertraum (05-432)
Manuel Blickle (JGU Mainz)
The EK correspondence (1)

Oberseminar Algebra und Geometrie
2026-02-02 16:45 - 17:45 | Frankfurt, Rober-Mayer-Str. 10, Raum 711 klein
Veronika Ertl (Universität Caen): Rigid syntomic cohomology over p-adic fields
Abstract: Syntomic cohomology plays an important role in the research of (p-adic) L-functions. An advantage of a rigid analytic approach is that it gives an explicit description suitable for calculations. On the other hand, it is rather technical, which makes laying down the foundations challenging. In this talk I will report on joint work in progress with Kazuki Yamada. I will explain how to extend the theory that we have previously developed of a syntomic cohomology for semistable schemes to the case of varieties over p-adic fields.

Tame Local Langlands
2026-02-03 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 13: The geometry of the stack of local Langlands parameters
Yifei Zhao (University of Münster)
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

p-adic Simpson correspondence
2026-02-04 14:00 - 18:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
Talk 11: Xinyu Shao (Leibniz Universität Hannover): The local correspondence
Talk 12: Dmytro Rudenko (Leibniz Universität Hannover): Canonical Higgs fields for pro-étale bundles

Riemann-Hilbert correspondence in characteristic p
2026-02-09 10:00 - 12:00 | Mainz, Hilbertraum (05-432)
Manuel Blickle (JGU Mainz)
The EK correspondence (2)

Workshop "Moduli in Heidelberg"
2026-02-10 13:00 - 2026-02-13 14:00 | Heidelberg, MATHEMATIKON, Konferenzraum, 5. OG, Campus Im Neuenheimer Feld (INF), INF 205, Heidelberg, 69120, Germany
Veronica Arena : TBA
Luca Battistella : Vector bundles on Olsson fans
Logarithmic geometry is a language that combines piecewise-linear and algebraic geometry, particularly useful for tracking the combinatorics of compactifications and degenerations of algebraic varieties. Olsson’s stack of logarithmic structures, and its charts provided by Artin cones, have played a fundamental role in moduli theory and enumerative geometry. Recent developments concerning stability, good moduli spaces, and logarithmic sheaf theory show the utility of considering Artin fans over a base, or Olsson fans. In joint work with Francesca Carocci and Jonathan Wise, we study their structure and vector bundles over them, generalising the theory of equivariant bundles on toric varieties. If time permits, I will discuss the relationship with Grassmannians and limit linear series that motivated our investigation.
Thomas Blomme : Correlated Gromov-Witten invariants & Multiple cover formula
Abelian surfaces are complex tori whose enumerative invariants seem to satisfy remarkable regularity properties. The computation of their reduced Gromov-Witten invariants in the case of primitive classes has already been well studied with many complete computations by Bryan-Oberdieck-Pandharipande-Yin. A few years ago, G. Oberdieck conjectured a multiple cover formula expressing in a very simple way the invariants for the non-primitive classes in terms of the primitive one. This would close the computation of GW invariants for abelian surfaces. In this second talk, we aim to explain how correlated invariants naturally show up in the decomposition formula for abelian surfaces, and how they allow to prove the multiple cover formula conjecture for many instances. This is joint work with F. Carocci.
Francesca Carocci : Correlated Gromov-Witten invariants & DR cycle formula
In this talk, we will talk about a geometric refinement for log Gromov -Witten invariants of P^1-bundles on smooth projective varieties, called correlated Gromov-Witten invariants, introduced in a joint work with T. Blomme. In order to compute them, we proved a correlated refinement of Pixton double-ramification cycle formula with target varieties. We will state the formula and try to give an idea of how it is obtained as an application of the Universal DR formula of Bae-Holmes-Pandharipande-Schmitt-Schwarz.
Aitor Iribar Lopez : TBA
Patrick Kenendy-Hunt : TBA
Navid Nabijou : Tautological projection of the Prym-Torelli locus
The moduli space of abelian varieties admits a tautological ring generated by lambda classes. In contrast to the space of stable curves, this tautological ring has a remarkably simple presentation. This allows for the construction of a canonical “tautological projection” which maps the full Chow ring onto the tautological subring, providing a left inverse to the inclusion of the latter in the former.
Given a Chow class on the moduli space of abelian varieties, it is natural to attempt to compute its tautological projection. For the Torelli locus (the locus of Jacobians) an algorithm was provided by Faber, the difficult step being integrating monomials in lambda classes on the space of stable curves.
We establish a corresponding algorithm for the Prym-Torelli locus (the locus of Prym varieties). The novel geometric content is a closed formula relating three different types of lambda classes (source, target, and Prym) on the moduli space of admissible covers, proved using Grothendieck-Riemann-Roch.
This is joint work in progress with Yoav Len and Sam Molcho.

Denis Nesterov : Hilbert-Chow crepant resolution conjecture
The conjecture in the title, proposed by Ruan, predicts that the quantum cohomology of Hilbert schemes of points on a surface is isomorphic to the orbifold cohomology of symmetric products. I will present a proof of the conjecture that relies on Fulton–MacPherson compactifications.

Sabrina Pauli : Tropical correspondence theorems for plane curve counts over arbitrary fields
We study the problem of counting rational curves of fixed degree on a toric del Pezzo surface subject to point conditions. Over algebraically closed fields, this count is invariant under the choice of point conditions. Over non-algebraically closed fields, however, the invariance fails. For real numbers, Welschinger’s groundbreaking work introduced a signed count of real curves that restores invariance.
Building on this, Levine and Kass-Levine-Solomon-Wickelgren have developed curve counts over arbitrary fields that not only generalize Welschinger’s signed counts and classical counts over algebraically closed fields, but also encode much richer arithmetic information.
In this talk I will survey these different approaches to counting rational curves with point conditions and discuss a recent joint result with A. Jaramillo Puentes, H. Markwig, and F. Röhrle. We establish a tropical correspondence theorem for curve counts over arbitrary fields, identifying the count of algebraic curves with point conditions with a weighted count of their tropical counterparts with point conditions. The latter are combinatorial objects and there are several purely combinatorial methods to find all tropical curves with point conditions.

Aaron Pixton : Cycles on universal Jacobians
Let J be the degree 0 universal Jacobian over the moduli space of smooth curves of genus g. Its Chow ring, CH(J), has an extra grading by weight (the Beauville decomposition). I will explain how to express the weight w part of CH(J) in terms of the Chow ring of a moduli space of curves with w marked points. This interpretation lets us translate ideas back and forth between cycles on universal Jacobians and cycles on moduli spaces of curves. Two consequences are a conjectural description of all tautological relations on universal Jacobians and a definition of a Fourier transform on moduli spaces of curves. I will also discuss how to extend this correspondence to compactified Jacobians over the moduli space of stable curves. This talk presents joint work with Younghan Bae.
Maximilian Schimpf : TBA
Pim Spelier : TBA
Calla Tschanz : From logarithmic Hilbert schemes to degenerations of hyperkähler varieties
In this talk, I will discuss my previous work on constructing explicit models of logarithmic Hilbert schemes. This relates to work or Li-Wu on expanded degenerations, Gulbrandsen-Halle-Hulek on degenerations of Hilbert schemes of points and Maulik-Ranganathan on logarithmic Hilbert schemes. The constructions I consider are local. I will then explain how we globalise these in joint work with Shafi and apply them to construct minimal type III degenerations of hyperkähler varieties, namely Hilbert schemes of points on K3 surfaces.

Angelina Zheng : The Brill-Noether rank and Martens’ theorem for tropical curves
Divisor theory on metric graphs has provided combinatorial proofs of several algebro-geometric results, most notably in Brill–Noether theory. In algebraic geometry, the dimensions of Brill–Noether loci play crucial roles, as in Martens’ theorem characterizing hyperelliptic curves. However, the tropical analogue of this result fails for metric graphs. Furthermore, the dimension of Brill–Noether loci does not vary upper semicontinuous in the moduli of tropical curves, as observed by C. M. Lim, S. Payne, and N. Potashnik. Motivated by this, D. Jensen and Y. Len conjectured that replacing the dimension with the Brill–Noether rank would yield a valid tropical analogue. However, this conjecture was later disproved by Coppens.
In this talk, based on joint work with G. Capobianco, I will discuss these counterexamples, and generalise them to a wider class of graphs. Finally, I’ll show that a suitably strengthened version of the conjecture holds for any graph.

Tame Local Langlands
2026-02-10 14:00 - 17:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 14: Weil-Deligne representations and discrete parameters
João Lourenço (Paris 13)
Explain Sections 2.1.4 and 2.1.5. Focus on the following aspects.
(1) Explain the stacks LocWD
LG,F and LocWLG,F and the isomorphism of the former one with LocLG,F . Explain the maps LocLG,F ∼= LocWD LG,F → LocWLG,F → Spf ZLG,F .
(2) Define (essentielly) discrete Langlands parameters (before Def. 2.28 and Def. 2.28 itself).
(3) Explain Prop. 2.32, Cor. 2.33. Mention Lemma 2.34.
Talk 15: The categorical local Langlands conjecture
Timo Richarz (TU Darmstadt)
Recall the theory of (ind)coherent sheaves (Chapter 9). Since we are happy
to restrict to the case that Λ = Q¯ℓ, we may assume that we are in the “classical”
characteristic zero case. Then state the categorical local Langlands conjecture.
Use the opportunity to summarized the first half the seminar.
The final session on February 10 will be a double session from 14:00 to 17:30, followed by dinner.
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

p-adic Simpson correspondence
2026-02-11 14:00 - 18:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
Talk 13: Margherita Recchia (Leibniz Universität Hannover): Proof of the correspondence
Talk 14: Simpson gerbe

Conference "Étale homotopy theory" - A conference on the occasion of Alexander Schmidt's 60th birthday
2026-03-09 - 2026-03-13 | Heidelberg, Mathematikon, SR tba

Oberseminar Algebra und Geometrie
2026-03-25 15:00 - 17:30 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
15:00 Uhr: Sara Sajadi (Universität Toronto): A Unified Finiteness Theorem For Curves
Abstract: This talk presents a unified framework for finiteness results concerning arithmetic points on algebraic curves, exploring the analogy between number fields and function fields. The number field setting, joint work with F. Janbazi, generalizes and extends classical results of Birch–Merriman, Siegel, and Faltings. We prove that the set of Galois-conjugate points on a smooth projective curve with good reduction outside a fixed finite set of places is finite, when considered up to the action of the automorphism group of a proper integral model. Motivated by this, we consider the function field analogue, involving a smooth and proper family of curves over an affine curve defined over a finite field. In this setting, we show that for a fixed degree, there are only finitely many étale relative divisors over the base, up to the action of the family’s automorphism group (and including the Frobenius in the isotrivial case). Together, these results illustrate both the parallels and distinctions between the two arithmetic settings, contributing to a broader unifying perspective on finiteness.
16:30 Uhr: Benjamin Steklov (Goethe Universität): Fermat’s Last Theorem for Selmer sections
Abstract: Wiles famously proved Fermat’s Last Theorem, which states that the (affine) Fermat curve of exponent p>2 has no rational points. Grothendieck’s section conjecture predicts that for a hyperbolic curve over a number field, rational points are controlled by sections of a natural exact sequence of étale fundamental groups. Combined with Fermat’s Last Theorem, this suggests that the corresponding sequence for the Fermat curve admits only sections arising from cusps. In this talk, we explain how to prove that this prediction holds for Selmer sections of the Fermat curve.

Junior Retreat
2026-04-07 - 2026-04-10 | Jugendherberge Limburg

de Rham-Witt complex
2026-04-13 10:15 - 11:45 | Mainz, Hilbertraum (05-432)
Timo Weiß: Introduction – Overview. Recollections on Witt vectors

Oberseminar K-Theorie
2026-04-15 10:15 - 11:45 | Mainz, 04-426
Abstract: Recent years have seen substantial progress in understanding algebraic K-theory of singular varieties. Still, computations of (higher) K-theory of singular varieties are quite rare, especially in dimension >1. In this talk, I will explain some techniques that allow one to perform computations in higher dimensions, with a particular focus on cubic surfaces and threefolds, where complete computations can be obtained in many cases.

Poincaré-Dualität in Charakteristik p
2026-04-16 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8, Heidelberg, Germany
Vortrag 1: Einführung – Immanuel Klevesath (Universität Heidelberg)

The K-theory of Z/p^n
2026-04-16 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 1: Introduction, background of K-theory and reduction steps – Marlon Kocher (Universität Heidelberg)

AGTZ-Kolloquium
2026-04-16 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Dominik Kirstein (JGU Mainz)
The signature as a map of cobordism categories
Abstract: The signature is a classical invariant of manifolds, which is a shadow of their intersection form. More refined topological indices of manifolds can be constructed by remembering the full intersection form.
In this talk, I will explain how the signature has an enhancement to a multiplicative map from geometric cobordism spectra of manifolds to algebraic cobordism spectra of Hermitian forms (known as Grothendieck-Witt or L-theory). This crucially depends on the construction of the signature on the level of cobordism categories. This approach generalises and unifies various existing constructions in the literature. I will conclude by explaining some interesting applications to geometric topology, such as a simple proof of the Weiss-Williams index theorem on characteristic classes of manifold bundles. Based on work in progress with Andrea Bianchi, Fabian Hebestreit, Kaif Hilman, Christian Kremer, Markus Land, Thomas Nikolaus and Wolfgang Steimle.

Symmetric Power Functoriality
2026-04-16 14:15 - 16:00 | Heidelberg
14:15 Talk 0: Alireza Shavali (Universität Heidelberg): Introduction

Oberseminar Algebra und Geometrie
2026-04-16 16:15 - 18:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
Valeria Bertini (Universita degli Studi di Milano) : Quotients of Hyperkähler manifolds

Abstract: Hyperkähler manifolds have been intensively studied from the 80s on, being building blocks of compact Kähler manifolds with trivial first Chern class; despite their natural role, finding examples of Hyperkähler manifolds is well known to be extremely challenging. In recent years, the focus has turned on their singular analogue, appearing naturally from the birational geometry perspective, and finally giving many new families of examples. A successful technique to produce singular examples is to consider (terminalizations of) quotients of smooth Hyperkähler manifolds. In this talk I will start presenting some recent results on singular Hyperkähler varieties constructed as quotients, and then I will turn to the case the quotient is a Calabi-Yau variety. The first part is a joint work with Grossi, Mauri and Mazzon, and the second one is work in progress with Garbagnati.

Wach modules of crystalline (phi, Gamma)-modules over the Robba ring
2026-04-17 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Janine Roshardt (ETH Zürich)
By works of Nathalie Wach and Laurent Berger there is an equivalence of Wach modules over B_Q_p^+ and crystalline p-adic representations of the absolute Galois group over Q_p. Jonathan Pottharst has stated a generalization of this equivalence to crystalline (phi, Gamma)-modules over the Robba ring, but no proof has appeared in the literature. In this talk, I will explain the ideas underlying this generalization and the construction of Wach modules over the positive Robba ring.

Seminar on Arithmetic Geometry
2026-04-17 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Nicolas Dupré (Wuppertal): 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 semisimple mod-p Langlands correspondence for GL_2(Q_p). Time permitting, we will also discuss some results about Ho(H) in higher rank.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)
