Locally analytic vector bundles on the Fargues-Fontaine-Curve
2025-04-24 11:15 - 13:15 (Europe/Berlin) | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
The adic Fargue-Fontaine curve
speaker: Max Witzelsperger (Heidelberg)

Berkovich motives
2025-04-24 13:00 - 13:30 | Darmstadt, Room 315 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 0: Overview (15min) ( Alberto Merici)

Berkovich motives
2025-04-24 13:30 - 15:00 | Darmstadt, Room 315 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 1: Motives (Christian Dahlhausen)

Holomorphic triple products
2025-04-24 14:00 - 16:00 | Mainz, Hilbertraum (05-432)
Jonas Stelzig (LMU München / JGU Mainz)
Abstract: I will introduce, and survey the context of, ABC triple Massey products, a holomorphic analogue of ordinary triple Massey products for complex manifolds. Then, I will discuss the (non)vanishing of these operations in situations of geometric interest, including toric, compact homogeneous Kähler, and Calabi Yau manifolds.

Berkovich motives
2025-04-24 15:30 - 16:30 | Darmstadt, Room 315 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 2: Cancellation Theorem (75min) ( Alberto Merici)

D-elliptic sheaves and the Hasse principle
2025-04-25 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Overview
Sriram Chinthalagiri Venkata (Heidelberg)
Begin by recalling Drinfeld’s theory of elliptic sheaves (or Shtukas) ([Mumford; Dri87]), andexplain briefly the importance of considering generalizations of them equipped with an action of D, namely D-elliptic sheaves. Then motivate and explain the main result in [Ara+24], by summarizing each talk of the seminar.

From p-adic Hodge theory to motivic cohomology and back
2025-04-25 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Tess Bouis (Universität Regensburg)
Abstract: The initial goal of p-adic Hodge theory, as formulated by the foundational conjectures of Fontaine in the 1980s, is to compare the different p-adic cohomology theories one can associate to schemes of mixed characteristic (0,p). If Fontaine’s conjectures have now been solved by the work of many people, the recent development of prismatic cohomology has shed new light on integral aspects of this theory. In this talk, I want to explain how one can use these recent advances in p-adic Hodge theory to construct a new theory of motivic cohomology for general (qcqs) schemes. This theory generalises the recent construction of Elmanto-Morrow over a field to mixed characteristic, and allows us to give a simplified motivic approach to certain classical results in p-adic Hodge theory. This is part of a joint work in progress with Arnab Kundu.

Seminar on Arithmetic Geometry
2025-04-25 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Zhixiang Wu (Universität Münster): Bernstein-Zelevinsky duality for locally analytic principal series representations
Bernstein-Zelevinsky duality is classically a duality on the derived category of smooth representations of a p-adic Lie group. In this talk, we will consider the Bernstein-Zelevinsky duality for locally analytic representations of p-adic Lie groups, and compute explicitly the duality for principal series representations. I will also explain the relationship of this duality with the duality of coherent sheaves on the (patched) eigenvariety. This is joint work with Matthias Strauch.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl

Motivic Spectra
2025-04-28 10:15 - 11:45 | Mainz, Hilbertraum (05-432) and Zoom
Talk 2: Thom-spaces (Timo Weiß)

Categorical Deligne–Langlands correspondence
2025-04-29 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 2: Michelle Klemt: Spaces of L-parameters
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

Algebraic proof of modular form inequalities for optimal sphere packings
2025-04-29 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Seewoo Lee (UC Berkeley)
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits)

Gromov-Witten theory and real enumerative geometry
2025-04-30 14:15 - 17:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
14:15 – 15:15 Talk 1: Andrei Bud (Universität Frankfurt): Real structures in low genus
15:45 – 16:45 Talk 2: Jeonghoon So (Universität Frankfurt): Counting coverings

D-elliptic sheaves and the Hasse principle
2025-05-02 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Stacks I
speaker: Chia-Fu Yu (Academia Sinica, Taiwan)

Seminar on Arithmetic Geometry
2025-05-02 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Christian Dahlhausen (Universität Heidelberg): Duality in (perfect) motivic homotopy theory
This talk treats a conjectured duality on modules over
K-theory in the stable homotopy category of a scheme whose dualising
object is given by G-theory. I shall explain a proof of the conjecture
for quasi-excellent schemes in characteristic zero. In order to approach
the conjecture in positive characteristic, I sketch the construction of
a “perfect motivic homotopy category” and compare it to the classical
homotopy category. For this perfect category, I shall sketch the proof
of an analogous version of the duality conjecture. This is joint work
with Denis-Charles Cisinski, Jeroen Hekking, and Storm Wolters.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl

Categorical Deligne–Langlands correspondence
2025-05-06 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Saskia Kern : Talk 3 – Derived categories of quasi-coherent sheaves
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

The Shintani–Faddeev modular cocycle: Stark units from q-Pochhammer ratios
2025-05-06 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Zhiyuan Li (SCMS, Fudan University)
The Shintani–Faddeev modular cocycle: Stark units from q-Pochhammer ratios
We give a new interpretation of Stark units associated to real quadratic fields as special “real multiplication values” of a modular cocycle described by complex meromorphic continuation of a simple infinite product. The cocycle encodes the modular transformations of the infinite q-Pochhammer symbol and is related to the Shintani–Barnes double sine funciton and the Faddeev quantum dilogarithm. As a corollary, we describe some intriguing features of the asymptotic behavior of the infinite q-Pochhammer symbol as the modular parameter approaches a real quadratic number.
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits)

Gromov-Witten theory and real enumerative geometry
2025-05-07 14:15 - 17:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
14:15 – 15:15 Talk 3: Nicole Müller (Universität Frankfurt): Shifted Symmetric functions and quasimodular forms
15:45 – 16:45 Talk 4: Lukas Schneider (Universität Frankfurt): Quick start to M g,n and its intersection theory

Locally analytic vector bundles on the Fargues-Fontaine-Curve
2025-05-08 11:15 - 13:15 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
(Equivariant) vector bundles
speaker: Otmar Venjakob (Heidelberg)

Anabelian geometry - Daniel Litt "Arithmetic representations of fundamental groups II"
2025-05-08 14:00 - 17:30 | Heidelberg
14:00 – 15:15 Talk 0: Marius Leonhardt (Universität Heidelberg): Introduction
15:45 – 17:00 Talk 1: Benjamin Steklov (Universität Frankfurt): Deformation spaces

Duality in (perfect) motivic homotopy theory
2025-05-08 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Christian Dahlhausen (Uni Heidelberg)
Abstract: This talk treats a conjectured duality on modules over K-theory in the stable homotopy category of a scheme whose dualising object is given by G-theory. I shall explain a proof of the conjecture for quasi-excellent schemes in characteristic zero. In order to approach the conjecture in positive characteristic, I sketch the construction of a “perfect motivic homotopy category” and compare it to the classical homotopy category. For this perfect category, I shall sketch the proof of an analogous version of the duality conjecture. This is joint work with Denis-Charles Cisinski, Jeroen Hekking, and Storm Wolters.

D-elliptic sheaves and the Hasse principle
2025-05-09 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
D-elliptic sheaves
speaker: Theresa Kaiser (Heidelberg)

Refined Chabauty–Kim computations for the thrice-punctured line over Z[1/6]
2025-05-09 13:30 - 14:30 | Heidelberg, Mathematikon, SR A and Livestream
Martin Lüdtke (MPIM Bonn)
Abstract: If X is a curve of genus at least 2 defined over the rational numbers, we know by Faltings’s Theorem that the set X(Q) of rational points is finite but we don’t know how to systematically compute this set. In 2005, Minhyong Kim proposed a new framework for studying rational (or S-integral) points on curves, called the Chabauty–Kim method. It aims to produce p-adic analytic functions on X(Q_p) containing the rational points X(Q) in their zero locus. We apply this method to solve the S-unit equation for S={2,3} and computationally verify Kim’s Conjecture for many choices of the auxiliary prime p.

Seminar on Arithmetic Geometry
2025-05-09 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Ferdinand Wagner (Universität Bonn): q-Hodge filtrations, Habiro cohomology, and THH over ku
The recent work of Garoufalidis, Scholze, Wheeler, and Zagier on the “Habiro ring of a number field” has sparked the question whether there exists a cohomology theory for smooth schemes over Z with coefficients in the Habiro ring, the completion of Z[q] at all roots of unity, and with specialisations to étale and de Rham cohomology. In this talk I’ll explain how this question is intimately related to the question whether the Hodge filtration on de Rham cohomology can be q-deformed to a filtration on q-de Rham cohomology. While such a q-deformed filtration (provably) doesn’t exist in general, I’ll explain how to construct a filtration (along with the “Habiro cohomology”) in many interesting cases, using topological Hochschild homology over the complex K-theory spectrum ku. I’ll also explain how a refined version of THH can be used to obtain a completely functorial construction for varieties over Q.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl

Theta series and tautological cycles on orthogonal Shimura varieties
2025-05-13 10:00 - 11:00 | Zoom
International Seminar on Automorphic Forms
Zhiyuan Li (Fudan university)
Theta series and tautological cycles on orthogonal Shimura varieties
In this talk, I will explore the fascinating interplay between lattice theory and vector- valued modular forms via theta series, presenting an elegant connection that bridges these areas. I will discuss its applications in the study of cycle theory on orthogonal Shimura varieties. One of our findings reveal that the Picard group of the Baily-Borel compactification of a broad class of Shimura varieties is isomorphic to ℤ. I will also explain the geometric motivation of this project. Most results are joint work with Huang, Müller and Ye.
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits)

Categorical Deligne–Langlands correspondence
2025-05-13 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Paul Siemon : Talk 4 – Self-duality of derived push forwards
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

Gromov-Witten theory and real enumerative geometry
2025-05-14 14:15 - 17:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
14:15 – 15:15 Talk 5: Moritz Frohwein (Universität Frankfurt): Cohomology of the moduli space of pointed rational curves
15:45 – 16:45 Talk 6.1: Miguel Prado (Universität Frankfurt): Moduli of stable maps I

Locally analytic vector bundles on the Fargues-Fontaine-Curve
2025-05-15 11:15 - 13:15 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Comparison to (φ, Γ)-modules
Marvin Schneider (Heidelberg)

Berkovich motives
2025-05-15 13:00 - 14:30 | Heidelberg, MATHEMATIKON, SR 12, INF 205, Heidelberg, BW, 69124, Germany
Talk 3: Berkovich spaces (Katharina Hübner)

Anabelian geometry - Daniel Litt "Arithmetic representations of fundamental groups II"
2025-05-15 14:00 - 17:30 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
14:00 – 15:15 Talk 2: Nils Witt (Universität Heidelberg): Basics on arithmetic representations
15:45 – 17:00 Talk 3: Alireza Shavali (Universität Heidelberg): Determinants à la Chenevier

On Voevodsky's reconstruction theorem
2025-05-15 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Sebastian Wolf (Regensburg)
In 1990, Voevodsky proved a conjecture of Grothendieck, that morphisms of normal schemes of finite type over the rational numbers can be reconstructed from the induced morphism of étale topoi. The goal of this talk is to give an outline of Voevodsky’s proof and explain a generalization of his result: Taking the étale topos is a fully faithful functor from finite type schemes over any finitely generated field to topoi over such a field after inverting univeral homeomorphisms. This is joint work with Magnus Carlson and Peter Haine.
