Seminar on Arithmetic Geometry
2026-05-29 15:30 - 17:00 (Europe/Berlin) | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Manuel Hoff (Bielefeld): Sheared displays and p-divisible groups
Abstract: Let p be a prime and let R be a p-nilpotent ring. The theory of displays, as developed by Zink and Lau, gives an equivalence between infinitesimal p-divisible groups and V-nilpotent displays over R. The aim of the talk is to explain that general p-divisible groups are equivalent to sheared displays, the analogue of displays where the ring of Witt vectors is replaced by its sheared version. This is joint work with Eike Lau.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

Membranes and Maps
2026-05-29 14:00 - 16:00 | Heidelberg, MATHEMATIKON, SR 007, Im Neuenheimer Feld 205, Heidelberg, 69120, Germany
In joint work with A. Brini, it was conjectured that equivariant Gromov–Witten invariants of Calabi–Yau fivefolds are governed by so-called membrane indices. When the fivefold is a product of a Calabi–Yau threefold and the affine plane, the latter invariants agree with, or refine, Gopakumar–Vafa invariants. I will present evidence for the conjecture. Moreover, I will explain how the numerical correspondence informs us about a possible modular interpretation of M2-branes since ultimately their moduli space should give rise to membrane indices. Building on ideas of Nekrasov and Okounkov, I will propose a geometric interpretation of M2-branes in some concrete situations. I will then translate this proposal into formulas for Hodge integrals, which can be verified in certain limits. This is based on work in progress with A. Giacchetto and R. Pandharipande.

AGTZ Kolloquium
2026-05-28 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Niklas Kipp (Paris-Sanclay)
A solid Syntomification
We will learn a strategy to obtain a well behaved six-functor formalism for Syntomic cohomology of p-adic formal schemes as defined by Bhatt-Morrow-Scholze. Here well behaved mainly refers to this six-functor formalism generalising Poincaré duality (which was proven by Longke Tang in the smooth and proper case) to smooth morphisms using a version of compactly supported syntomic cohomology. Concretely, we will recall some aspects of the stacky approach to Prismatic/Syntomic cohomology (following Bhatt-Lurie and Drinfeld) as well as some aspects of the theory of (Solid) analytic stacks (following Clausen-Scholze).

Kolloquium Geometrie und Arithmetik
2026-05-28 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Niklas Kipp (Paris-Saclay): A solid Syntomification
Abstract: We will learn a strategy to obtain a well behaved six-functor formalism for Syntomic cohomology of p-adic formal schemes as defined by Bhatt-Morrow-Scholze. Here well behaved mainly refers to this six-functor formalism generalising Poincaré duality (which was proven by Longke Tang in the smooth and proper case) to smooth morphisms using a version of compactly supported syntomic cohomology. Concretely, we will recall some aspects of the stacky approach to Prismatic/Syntomic cohomology (following Bhatt-Lurie and Drinfeld) as well as some aspects of the theory of (Solid) analytic stacks (following Clausen-Scholze).

Oberseminar Algebra und Geometrie
2026-05-27 16:00 - 18:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
Konstantinos Kartas (Universität Münster): Taming perfectoid algebras
Abstract: The almost purity theorem is a foundational result in perfectoid geometry which, as the name suggests, holds only in an “almost” sense. We aim to identify a class of rings for which the theorem holds in a genuine (non-almost) form. Joint work in progress with Franziska Jahnke.

Seminar on Arithmetic Geometry
2026-05-22 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Lucien Hennecart (CNRS): The BPS sheaf for preprojective algebras and moduli of Higgs bundles
In the first part of the talk, I will introduce the BPS sheaf associated with the preprojective algebra of a quiver. This is a perverse sheaf on the moduli space of representations, endowed with a Lie algebra structure, which encodes the Kac polynomials of the quiver. Its structure is described in terms of generators and relations in joint work with Davison and Schlegel Mejia. This description is formulated in terms of a generalized Kac–Moody algebra.
In the second part, I will explain how this description makes it possible to determine the supports and local systems of the direct summands of the BPS sheaf. This description involves the geometry of hypertoric varieties in general, and can in certain cases be simplified. Applying these results to the Hitchin fibration, one recovers results due to de Cataldo, Heinloth, Migliorini, and also Mauri, concerning the effective decomposition theorem for the Hitchin morphism involving Ngo strings. This is all based on various discussions with Ben Davison.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

Toward the noncommutative minimal model program
2026-05-22 14:00 - 16:00 | Heidelberg, MATHEMATIKON, SR 007, Im Neuenheimer Feld 205, Heidelberg, 69120, Germany
The aim of the talk is to introduce the noncommutative minimal model program (ncMMP) proposed by Halpern-Leistner and inspired by some works of Dubrovin and Kontsevich. For a given projective variety X, the classical minimal model program asks if there is a variety Y that is birational to X but has simpler geometry, such Y is called a minimal model of X. In the noncommutative context, we consider the derived category D(X) of coherent sheaves on X, and we ask if we can decompose it canonically. The biggest factor of the decomposition is then a minimal model for D(X). In order to find such a decomposition Halpern-Leistner proposes to use the quantum cohomology of X.
We will discuss some examples where Halpern-Leistner’s proposal is satisfied: Grassmannians, quadrics, and cubics in dimensions 3 and 4.

Construction of logarithmic cohomology theories
2026-05-22 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Doosung Park (Wuppertal)
In this talk, I will explain a functor extending cohomology theories from schemes to log schemes. Using this functor, we can obtain the log cyclotomic trace, and we can represent K-theory in the logarithmic motivic homotopy category. I will also explain an application to the p-adic deformation problem for the K-theory of semistable schemes.

AGTZ Kolloquium
2026-05-21 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Marc Hoyois (Uni Regensburg)
Poincaré localizing invariants of schemes
In joint work with Markus Land, we investigate motivic properties of Poincaré localizing invariants of schemes, like Grothendieck-Witt theory, and we establish that they satisfy a projective bundle formula and descent for the Nisnevich topology. This implies that the motivic sphere spectrum over (almost) any local ring R admits a faithful action of the Grothendieck-Witt group of nondegenerate symmetric bilinear forms over R.

Oberseminar Algebra und Geometrie
2026-05-18 16:00 - 18:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
Michael Temkin (MPI Bonn): Wild Hurwitz spaces and level structures

Abstract: Hurwitz moduli spaces of covers of curves of degree d are classical and well studied objects if one assumes that d! is invertible and hence no wild ramification phenomena occur. There were very few attempts to study the wild case. In the most important one Abramovich and Oort started with the classical space H_{2,1,0,4} of double covers of P^1 ramified at four points and (following an idea of Kontsevich and Pandariphande) described its schematic closure H in the space of stable maps over Z. The result over F_2 was both strange and informative, but lacked a modular interpretation.
In the first part of my talk I will describe the example of Abramovich-Oort and then tell about a work in progress of Hippold, where a (logarithmic) modular version of compactified Hurwitz space of degree p is constructed when only (p-1)! is invertible. In particular, this conceptually explains phenomena observed by Abramovich-Oort. In the second part I will describe another outcome of the same ideas. It was observed by Abramovich-Oort that H is the blowing up of the modular curve X(2). This is not a coincidence, and the same ideas can be used to refine the wild level structures of Drinfeld and construct modular interpretation of the minimal modifications of the curves X(p^n) which separate ordinary branches at any supersingular point. This is a very recent work in progress and the precise description of the obtained spaces is still to be found.

AGTZ-Kolloquium
2026-05-12 12:30 - 13:30 | Mainz, Hilbertraum (05-432)
Carl Mautner (University of California, Riverside, USA)
Hilbert schemes, perverse sheaves and a new Schur algebra
The Schur algebra is a finite-dimensional algebra that connects the representation theory of the symmetric and general linear groups. In joint work with Tom Braden, we give an algebraic description of the category of perverse sheaves with coefficients in a field of characteristic p on S^n(C^2), the n-fold symmetric product of the plane, in terms of a new, enhanced version of the Schur algebra. This work is motivated by a geometric description of the standard Schur algebra and the theory of symplectic duality.

Syntomic descent spectral sequence for arithmetic p-adic varieties
2026-05-08 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Yicheng Zhou (Paris-Saclay)
For a “large” class of rigid-analytic varieties over a p-adic local field, we explain how to construct a natural syntomic descent spectral sequence compatible with the Hochschild-Serre spectral sequence. As a consequence, for proper rigid-analytic varieties, the étale regulators maps on suitable K-theoretic groups factor through their syntomic counterparts, for suitably defined syntomic Chern class maps.

CRC-Colloquium
2026-05-07 15:30 - 18:30 | Darmstadt
15:00 Coffee
15:30 – 16:30 Sabrina Pauli (TU Darmstadt): Tropical and Arithmetic Perspectives
16:30 Coffee and Cake
17:00 – 18:00 Jakob Stix (Goethe Universität Frankfurt): The Anabelian Section Conjecture
18:30 Dinner

Seminar on Arithmetic Geometry
2026-04-24 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Lucas Gerth (IMJ Paris): Moduli spaces of analytic p-divisible groups
Abstract: We prove a classification of families of analytic p-divisible groups on adic spaces S over Qp in terms of Hodge–Tate triples on S, generalizing a theorem of Fargues. From this, for S a perfectoid space, we construct an analytic Dieudonné theory with values in mixed characteristic Shtukas over the Fargues–Fontaine disc. As applications, we realize the local Shimura varieties of EL and PEL type of Scholze–Weinstein as moduli spaces of analytic p-divisible groups with framed universal cover, and we reinterpret the Hodge–Tate period map of Scholze in terms of topologically p-torsion subgroups of abelian varieties.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

Variation of crepant resolutions of Kleinian singularities
2026-04-24 14:00 - 16:00 | Heidelberg, MATHEMATIKON, SR 007, Im Neuenheimer Feld 205, Heidelberg, 69120, Germany
The McKay correspondence establishes a strong relationship between the classical minimal resolution and the standard orbifold resolution of a Kleinian surface singularity. Based on joint work with Ruth Wye, I will explain how the McKay correspondence extends to a larger class of crepant stacky resolutions of the singularity, and how their Hilbert schemes of points are related through variation of GIT quotients (VGIT). Time permitting, I will also sketch some recent ideas from work in progress with Austin Hubbard on how to relate the resolutions themselves via VGIT by taking into account the variation of monoidal structures on their mutual derived category.

Duality for the condensed cohomology of the Weil group of a p-adic field
2026-04-24 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Marco Artusa (CIRM (Luminy) and I2M (Marseille))
Duality theorems are among the central results in arithmetic geometry. For $p$-adic fields, the earliest example is due to Tate, dealing with Galois cohomology of finite Galois modules. To extend this result to more general coefficients, one is forced to modify the original cohomology groups. This underlines some shortcomings of Galois cohomology, such as the lack of a natural topology on cohomology groups. In this talk, we build a new topological cohomology theory for p-adic fields, thanks to the Weil group and Condensed Mathematics. Moreover, we see how to use this cohomology theory to extend Tate’s result to more general topological coefficients. This new duality takes the form of a Pontryagin duality between locally compact abelian groups. As a particular case, one gets the reciprocity isomorphisms of local class field theory “à la Weil”, which identifies the units of a $p$-adic field and the abelianised Weil group. One could try to apply similar techniques to higher local fields. Inspired by Kato’s work, the hope is to obtain a condensed-Weil version of higher local class field theory, which would identify $d$-th Milnor $K$-theory of a higher local field with its abelianised Weil group.

AGTZ Kolloquium
2026-04-23 14:15 - 15:15 | Mainz, Hilbertraum 05-432
Kaif Hilmann (Uni Bonn)
Titel: Equivariant localizing motives for finite groups and applications
Abstract: In this talk, I will give a proposal for a definition of genuine equivariant lozalizing motives for finite groups G. Using isotropy separation arguments on equivariant cubes and the recent insights of Ramzi-Sosnilo-Winges, we use this version of motives to enhance the algebraic K-theory functor with the structure of multiplicative norms.
Among other things, we use our results to give a new and much simplified proof that K-theory admits polynomial functoriality, first proved in a celebrated paper of Barwick-Glasman-Mathew-Nikolaus. Time permitting, we will also discuss other applications such as constructing an equivariant Dennis trace map and showing that all genuine G-spectra are the K-theory of a G-stable category. This reports on joint work with Maxime Ramzi.

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)

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.

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.

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.

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.

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.

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.

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)

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.

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)

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)

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)

Conformal Field Theory
2026-01-16 14:00 - 18:00 | Darmstadt, Room S1|03 226, Hochschulstraße 1, Darmstadt, Germany
14:00-15:00: Anne Moreau (Laboratoire de Mathématiques d’Orsay): W-algebras as conformal extensions of affine vertex algebras
15:15-16:15: Quan Situ (Clermont Auvergne University): Extension between simple and costandard modules in the modular BGG category O
17:00-18:00: Lennart Meier (Utrecht University): From conformal field theories to topological modular forms
