CRC 326 - GAUS

Conference: Vertex algebras, automorphic forms and combinatorics
2026-06-01 - 2026-06-05 | Marseille
For more information see
https://conferences.cirm-math.fr/3656.html

de Rham-Witt complex
2026-06-01 10:15 - 11:45 (Europe/Berlin) | Mainz, Hilbertraum (05-432)
Timon Tausendpfund
§6: Seminormal aspects
The de Rham–Witt complex is invariant under semi-normalization (and recovers the semi-normalization of a ring). Cover §§6.1-6.2 and §§6.5-6.6, with a focus on Proposition 6.2.1, Corollary 6.5.2, and Theorem 6.5.3. As time permits, introduce crystalline cohomology (as the cohomology of the structure sheaf on the crystalline site relative to the divided power ring (Zp,(p)), see for example the book by Berthelot or Tag 07GI in the Stacks project) and cover §6.4.

International Seminar on Automorphic Forms
2026-06-02 16:00 - 17:00
Spectral theory of automorphic forms: infinite co-volume.
Chris Lutsko (University of Houston)
Given a Lie group G and a discrete subgroup Γ<G, a critical tool used to analyze automorphic forms is to use spectral decomposition (e.g Selberg trace formula). For rank one hyperbolic manifolds the spectrum is either well understood or far beyond reach (e.g Selberg eigenvalue conjecture). In infinite volume the spectrum becomes linked to interesting geometric features of the manifold. In this talk I will survey some results about the spectrum of infinite co-volume subgroups and the connection to geometry and representation theory. This will include work with Dubi Kelmer and Alex Kontorovich, as well as work with Tobias Weich and Lasse Wolf.
Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).

Specialization of iterated Galois groups
2026-06-03 14:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 308
14:00 – 15:15 Talk 3: Ruth Wild (Goethe Universität Frankfurt): Extension of the base field – part I
15:45 – 17:00 Talk 4: Magnus Carlson (Goethe Universität Frankfurt): Extension of the base field – part II

de Rham-Witt Complex
2026-06-08 10:15 - 11:45 | Mainz, Hilbertraum (05-432)
Anton Engelmann
Derived considerations
The Nygaard filtration and foundations for the last four talks. Define filtered derived categories (Construction 8.4.1) and the Beilinson t-structure (Remark 8.4.8). Use Proposition 8.4.10 as a definition for the functor Lηp, and give a more explicit description relating it to the functor ηp of §2.1. Discuss Proposition 7.2.4, Theorem 7.4.7 and Corollary 7.4.8. Finally, define the Nygaard filtration as in Proposition 8.4.11. As time permits, come back to some descriptions and properties in §8.1 and §8.2.

International Seminar on Automorphic Forms
2026-06-09 16:00 - 17:00
tba
Hassan Saad (LSU)
Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).

Specialization of iterated Galois groups
2026-06-10 14:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 308
14:00 – 15:15 Talk 5: Leonie Nienhaus (Goethe Universität Frankfurt): Proof of theorems 1.2 and 1.3
15:45 – 17:00 Talk 6: Benjamin Steklov (Goethe Universität Frankfurt): Proof of theorem 1.4

Poincaré-Dualität in Charakteristik p
2026-06-11 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8, Heidelberg, Germany
Vortrag 7: Dimension der Kohomologiegruppen – Alexander Schmidt

WKB Analysis: From Quadratic Differentials to Stokes matrices
2026-06-11 10:00 - 12:30 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
10:00 – 11:00 Talk 7: Paul Siemon (TU Darmstadt): SL(n, C)-Opers
11:30 – 12:30 Talk 8: Johannes Horn (Goethe Universität): SL(n, C)-spectral networks and WKB analysis for opers

The K-theory of Z/p^n
2026-06-11 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 7: Generators and relations descriptions for the Nygaard filtration –
Otmar Venjakob (Universität Heidelberg)

AGTZ Kolloquium
2026-06-11 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Calla Tschanz (Uni Bochum)
Title:
From logarithmic Hilbert schemes to degenerations of hyperkähler varieties
Abstract:
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.

Symmetric Power Functoriality
2026-06-11 14:15 - 16:00 | Heidelberg
14:15 Talk 6 Deforming Global Galois Representations: Nils Tietke

Eisenstein Congruences at Prime-Square Level
2026-06-12 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Jaclyn Lang (Temple University Philadelphia)
In Mazur’s celebrated Eisenstein ideal paper, he studies congruences between prime-level cusp forms and the unique weight-2 Eisenstein series of the same level. He shows that (if p is at least 5) such mod-p congruences exist if and only if the level N is congruent to 1 modulo p. In this talk, we consider Eisenstein–cuspidal congruences in weight 2 and level N2, still under the condition that N = 1 mod p. In this case, recent work with Pollack and Wake shows that the relevant level-N2 Hecke algebra is a free module over an appropriate inertia-at-N pseudodeformation ring. This structure turns out to be surprisingly powerful. One can recover Mazur’s existence theorem that there exists a mod-p Eisenstein–cuspidal congruence in weight 2 and prime level N when N = 1 mod p. One can also recover the results of Merel and Lecouturier that characterize the rank of Mazur’s Hecke algebra in terms of the order of vanishing of a certain zeta element in cases when that rank is at most 3. We will discuss some of the ideas that go into these results. In addition to the joint work with Pollack and Wake, the later results are joint with Palvannan and Müller.

Crossed instantons in algebraic geometry
2026-06-12 14:00 - 16:00 | Heidelberg, MATHEMATIKON, SR 007, Im Neuenheimer Feld 205, Heidelberg, 69120, Germany
In a series of papers, Nekrasov introduces moduli spaces of “crossed instantons,” certain quiver representations modeling instantons on unions of 2-planes in 4-space. The geometry of these spaces encodes information about moduli of sheaves on surfaces and produces deformations of characters of quantum affine algebras. In work with Martijn Kool and Woonam Lim, we study Nekrasov’s moduli spaces from the perspective of algebraic geometry. I’ll explain how invariants of moduli spaces of crossed instantons can be defined using a construction from sheaf-counting on Calabi-Yai 4-folds. I’ll also state a speculative description of these spaces as moduli spaces of framed sheaves on a projective 4-fold.

Seminar on Arithmetic Geometry
2026-06-12 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Federico Binda (Milano): On the p-adic deformation of K-theory classes
In this talk I will survey some recent results around generalizations of the Beilinson-Bloch-Esnault-Kerz fiber square, relating the algebraic K-theory of a scheme to its topological cyclic homology. In particular, I will discuss how log geometry naturally enters the picture in the case of bad reduction, and how one can control the obstruction to lifting K-theory classes in the semistable case using the “Hyodo-Kato Chern character”, extending the work of Antieau-Mathew-Morrow-Nikolaus. The methods involve some reduction from the logarithmic to the non logarithmic case, using some results of motivic origin in the non-A^1-invariant setting.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

de Rham-Witt Complex
2026-06-15 10:15 - 11:45 | Mainz, Hilbertraum (05-432)
Klaus Mattis
§9: The derived de Rham-Witt complex 1/2
Alternative description of the de Rham–Witt complex. More general criterion for when it can recover the de Rham complex. Define the derived de Rham–Witt and derived de Rham complexes (Construction 9.2.5, Variant 9.2.6) and the conjugate filtration (Remark 9.2.7). Discuss Theorem 9.3.1 (the saturated de Rham–Witt complex in terms of the derived one). Prove Corollary 9.3.5 as an application. Prove Theorem 9.4.1 and Proposition 9.4.6.

International Seminar on Automorphic Forms
2026-06-16 16:00 - 17:00
A Geometric Approach to Ki’s L4 Norm Bound
Trajan Hammonds (Aarhus)
The behavior of L^p norms of automorphic forms is a central topic in analytic number theory. In 2023, Haseo Ki proved the Iwaniec-Sarnak conjecture for L4 norms for Hecke-Maass cusp forms, long thought to be out of reach. In this talk, I will present joint work with Anshul Adve, along with work of Paul Nelson, providing a new proof of Haseo Ki’s optimal L4 norm bound. The key novelty is avoiding a hands-on analysis of Bessel function asymptotics, at least in the critical range. Instead we are able to recast the essential estimates into a simple problem in incidence geometry and solve it.
Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).

Poincaré-Dualität in Charakteristik p
2026-06-18 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8, Heidelberg, Germany
Vortrag 8: Gerstenauflösung I – Immanuel Klevesath

The K-Theory of Z/p^n
2026-06-18 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 8: Relative-to-absolute descent II – Chenyi Yang (Universität Heidelberg)

Cohomology of symmetric stacks
2026-06-18 14:00 - 16:00 | Heidelberg, MATHEMATIKON, SR 007, Im Neuenheimer Feld 205, Heidelberg, 69120, Germany
I will talk about a joint project with Chenjing Bu, Ben Davison, Andrés Ibáñez-Núñez, and Tasuki Kinko. For a large class of stacks, we decompose their cohomology in terms of what we call BPS cohomology, which is a structure originating in enumerative geometry of Calabi-Yau 3-folds, but which is of interest beyond this class of examples. Such stacks include smooth stacks (such as the moduli of G-bundles on a curve), symplectic stacks (such as the moduli of G-Higgs bundle on a curve), or some (-1)-shifted symplectic stacks (such as the moduli of semistable sheaves on a Calabi-Yau threefold).

Oberseminar Algebra und Geometrie
2026-06-18 16:00 - 18:00 | Frankfurt, RM-Str. 6-8, R. 308
Dr. Giusi Capobianco: Algebraic and tropical Prym-Torelli map
Abstract: Given an étale double cover of smooth curves one can associate a principally polarized abelian variety called the Prym variety. The map from the moduli space of double covers Rg to the moduli space of pp abelian varieties Ag-1 is called Prym-Torelli, in analogy with the Jacobian case. This map does not extend to a morphism from the boundary of Rg to any of the standard toroidal compactifications of Ag-1. In this talk I will present their tropical counterpart and prove that, with a slight modification of the definition, the tropical Prym-Torelli map is continuous.
This result is part of my PhD thesis and will appear on the arXiv soon.

AGTZ Kolloquium
2026-06-18 16:30 - 17:30 | Mainz, Hilbertraum (05-432)
Karin Schaller (JGU Mainz)
Titel: Nobodies are perfect, semigroups are not.
Newton-Okounkov bodies provide a powerful link between algebraic geometry and convex geometry, extending the correspondence between toric varieties and lattice polytopes. They are constructed from valuation semigroups associated with divisors, making the finite generation of these semigroups a natural and important question. After an introduction to toric geometry, we study valuation semigroups on toric surfaces arising from non-toric flags. Based on joint work with Altmann, Haase, Küronya, and Walter, the talk presents a combinatorial criterion for the finite generation of these semigroups.

On arithmetical surjectivity and the Conjecture of Colliot-Thelene
2026-06-19 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Florian Pop (University of Pennsylvania)
The notion of ‘arithmetical surjectivity’ (a.s.) for dominant morphisms f of proper smooth varieties over number fields was introduced by Colliot-Thelene, and he made a precise
conjecture (CCT) relating a.s. to birational properties of the morphisms f. The CCT was proved in a sharper form by Denef (2019), and Loughran-Skorobogatov-Smeets gave a
characterization of a.s. (2020). I will present a new method of proof which allows generalizations/refinements of the above results by: First, allowing k to be any finitely generated base fields k with char(k)=0 (and beyond). Second, showing that a.s. is a fully birational property, i.e., a.s. depends only on properties of the function field extension defined by morphisms f. The method of proof also yields generalizations of the so called
zero-cycle surjectivity, considered/characterized over number fields by Gvirtz (2020).
NOTE: The problems are completely open in positive characteristic!

Seminar on Arithmetic Geometry
2026-06-19 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Louisa Bröring (Duisburg-Essen): Quadratic Euler Characteristic of Geometrically Cyclic Branched Coverings
The quadratic Euler characteristic $chi(X)$ of a smooth, projective scheme
$X$ over a field $k$ of characteristic not two is a refinement of the
topological Euler characteristic to quadratic forms, constructed using motivic
homotopy theory. For example, if $ksubset mathbb{R}$, then rank of $chi(X)$
is equal to the topological Euler characteristic of $X(mathbb{C})$ and the
signature of $chi(X)$ with respect to the given embedding is equal to the
topological Euler characteristic of $X(mathbb{R})$. The quadratic Euler
characteristic plays an import role in the programme of $mathbb{A}^1$-refined
enumerative geometry.
After briefly introducing the quadratic Euler characteristic, we present a
computation of the quadratic Euler characteristic of geometrically cyclic
branched coverings leveraging Levine’s quadratic Riemann-Hurwitz formula. An
$n$-fold geometrically cyclic branched covering is a morphism $fcolon Y to
X$ between smooth, projective schemes together with a smooth, closed subscheme
$Z subset X$ satisfying the following condition: there exists a line bundle
$L$ over $X$ and a section $s colon X to L^{otimes n}$ such that $Z$ is the
zero locus of $s$ and $f$ is the pullback along $s$ of the map $L to
L^{otimes n}$ taking $n$-th powers.
As an application, we compute the quadratic Euler characteristic of branched
double covers of $mathbb{P}^2$, which includes some K3 surfaces.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

de Rham-Witt complex
2026-06-22 10:15 - 11:45 | Mainz, Hilbertraum (05-432)
Daniel Fink
§9: The derived the Rham-Witt complex 2/2
By the criterion of the previous talk, the de Rham–Witt complex recovers the de Rham complex for a more general class of rings. Cover §9.5, in particular Theorem 9.5.6, Corollary 9.5.19, and Theorem 9.5.21.

International Seminar on Automorphic Forms
2026-06-23 16:00 - 17:00
Zeros of Poincaré series
Noam Kimmel (MPIM Bonn)
We explore the zeros of certain Poincaré series P(k,m) of weight k and index m for the full modular group. These are distinguished modular forms, which have played a key role in the analytic theory of modular forms. We study the zeros of P(k,m) when the weight k tends to infinity. The case where the index m is constant was considered by Rankin who showed that in this case almost all of the zeros lie on the unit arc |z|=1. In this talk we will explore the location of the zeros when the index m grows with the weight k, finding a range of different limit laws. Along the way, we also establish a version of Quantum Unique Ergodicity for some ranges.
Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).

Oberseminar Algebra und Geometrie
2026-06-24 14:00 - 16:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 308
Jonas Heintze (Universität Bonn): Poincare duality for Fargues Fontaine curve with almost coefficients
Abstract: The Fargues-Fontaine curve is a central geometric object in modern approaches to p-adic Hodge theory. In this talk, we will sketch ongoing work aimed at establishing Poincaré duality for the Fargues-Fontaine curve(s) viewed as analytic stacks using almost mathematics. This work is closely related to recent work of Anschütz, Le Bras, and Mann.

Poincaré-Dualität in Charakteristik p
2026-06-25 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8, Heidelberg, Germany
Vortrag 9: Gerstenauflösung II – Alberto Merici

The K-Theory of Z/p^n
2026-06-25 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Talk 9: Relative-to-absolute descent III – Chenyi Yang (Universität Heidelberg)

AGTZ Kolloquium
2026-06-25 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Shai Keidar (Uni Regensburg)
Title: pi-finite Galois theory
Abstract: In the higher-categorical world, Galois theory extends beyond finite groups: one can study Galois extensions for an arbitrary E_1-group. We develop such a theory for higher semiadditive categories, where finite groups are naturally replaced by pi-finite groups. Under height assumptions, we construct an n-truncated pro-pi-finite “absolute Galois group” representing all Galois extensions, and develop a higher Kummer theory relating abelian extensions to the Picard spectrum. As an illustration, we attach a pro-pi-finite Galois space to a rational Stefanich ring and give an algorithm computing it.
