CRC 326 - GAUS

Shtukas for reductive groups and global Langlands correspondence after Vincent Lafforgue
2024-06-14 09:00 - 11:00 (Europe/Berlin) | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 8: Sriram C. Venkata: Specialization to the diagonal (Part I)

Anabelian geometry
2024-06-13 14:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
14:00 – 15:15 Talk 4: Leonie Scherer (Goethe Universität): Belyi’s theorem and tangential base-points
Coffee break
15:45 – 17:00 Talk 5: Marcin Lara (Goethe Universität): Consequences of Belyi’s theorem, direct sums and tensor products

Arithmetic of critical p-adic L-functions
2024-06-13 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 7: Rustam Steingart: Big Galois representations

Purity for the flat cohomology
2024-06-13 09:15 - 10:45 | Heidelberg, Mathematikon, SR tba
Talk 5: Tim Holzschuh (Universität Heidelberg): Introduction to animated rings and cohomology of affine smooth groups (Part 1)

A gentle introduction to non-abelian Hodge and P=W conjecture
2024-06-12 16:00 - 18:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Oberseminar Algebra und Geometrie
Alexandre Minets (MPI Bonn)
Abstract:
Title: A gentle introduction to non-abelian Hodge and P=W conjecture
Abstract: Let C be a Riemann surface, and M_B the character variety of C; in other words, the points of M_B parameterise representations of the fundamental group of C. Up to a _non-algebraic_ homeomorphism, M_B can also be realized as the variety M_H of algebraic vector bundles on C equipped with a twisted endomorphism (otherwise known as Higgs bundles). The P=W conjecture of de Cataldo-Hausel-Migliorini postulates that some algebraic data survives the homeomorphisms above; more precisely, the number of F_q-points of M_B is controlled by an algebraic integrable system on M_H. I will give a gentle introduction to these objects, focusing on one explicit example. If time permits, I will sketch some ideas that went into our recent proof of P=W (joint with T. Hausel, A. Mellit, O. Schiffmann).

On the denominators of the special values of the partial zeta functions of real quadratic fields
2024-06-11 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Hohto Bekki (MPIM Bonn)
It is classically known that the special values of the partial zeta functions of real quadratic fields, or more generally, of totally real fields at negative integers are rational numbers. In this talk, I would like to discuss the denominators of these rational numbers in the case of real quadratic fields. More precisely, Duke recently presented a conjecture which gives a universal upper bound for the denominators of these special values of the partial zeta functions of real quadratic fields. I would like to explain that by using Harder’s theory on the denominator of the Eisenstein class for SL(2,Z), we can prove the conjecture of Duke and moreover the sharpness of his upper bound. This is a joint work with Ryotaro Sakamoto.
https://tu-darmstadt.zoom.us/j/68048280736

Chromatic Homotopy Theory
2024-06-11 14:00 - 15:30 | Darmstadt, Room 401, Mainz Room 04-432 and Zoom, Darmstadt and Mainz, Darmstadt and Mainz
Lucas Gerth (Uni Frankfurt)
Talk 9* – Lubin–Tate theory
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number

Conference: Vertex algebras, geometric representation theory and quantum groups
2024-06-10 - 2024-06-14 | Marseille
For more information see
https://conferences.cirm-math.fr/3045.html

Seminar on Arithmetic Geometry
2024-06-07 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Minjia Zhang (Princeton University): Igusa stacks and cohomology of Shimura varieties
Shimura varieties have been playing an important role in the Langlands program. Recently, following a conjecture of Peter Scholze, we have constructed certain p-adic geometric objects, which we call ​”Igusa stacks” (in the PEL type case), which encode prime-to-p information of Shimura varieties. Together with certain flag varieties (encoding information of Shimura varieties at p), they give p-adic uniformization of Shimura varieties. In this talk, I will explain construction of Igusa stack for Hodge type Shimura varieties, which leads to new proofs of Mantovan’s product formula, Eichler-Shimura relations, and vanishing type results about torsion cohomology of Shimura varieties. This is based on joint work with Patrick Daniels, Daniel Kim and Pol van Hoften.
Zoom 635 7328 0984, Kenncode: kleinste sechsstellige Primzahl

Zagier’s conjecture on polylogarithms: from function fields to number fields
2024-06-07 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Quentin Gazda (CMLS Palaiseau)
Zagier’s conjecture is a certain formulation of the following slogan: linear relations among polylogarithms evaluated at algebraic numbers arise from relations between K-theory symbols. By identifying the different attributes of this conjecture, one can state and prove a similar version in arithmetic of function fields. Classical polylogarithms are then replaced by those of Carlitz. The proof, very different from the techniques developed so far, uses ingredients from the theory of difference equations. It involves deformations of Carlitz polylogarithms where a new variable $t$ appears. This results from a joint work with A. Maurischat.
While we currently lack the technology to reproduce this argument in number theory, it is amusing to speculate on a hypothetical transcription. $q$-deformations of polylogarithms then replace these « $t$-deformations ». With T. Bouis, we recently encountered versions of $q$-polylogarithms in the syntomic Chern class introduced by Bhatt-Lurie. This is encouraging…! I will mention these works in a second part of the presentation.

Shtukas for reductive groups and global Langlands correspondence after Vincent Lafforgue
2024-06-07 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 7: Alireza Shavali (Universität Heidelberg): Finiteness of cohomology of moduli of shtukas

CRC-Colloquium
2024-06-06 15:30 - 18:30 | Darmstadt Gebäude S1|15, Hörsaal 133
15:20 Coffee (or earlier)
15:30 – 16:30 Georg Tamme (Universität Mainz): Higher algebra and K-theory
16:30 Coffee and Cake
17:15 – 18:15 Otmar Venjakob (Universität Heidelberg): Explicit Reciprocity Laws in Number Theory
18:45 Dinner
Abstract G. Tamme:
Algebraic K-theory, more precisely the group K_0(X) of a scheme X, was first introduced by Grothendieck in order to formulate and prove a very general Riemann-Roch theorem. Subsequently, lower (i.e. K_i for i<0) and higher (i.e. K_i for i>0) K-groups have been introduced by Bass, Milnor, Quillen, and Thomason. They have turned out to be a rich invariant, playing an important role in various fields such as number theory and topology. Although explicit computations of K-groups remain challenging, modern methods from higher algebra and derived algebraic geometry have led to several breakthrough structural results concerning these groups. In the talk, I will give an introduction to these topics and, time permitting, discuss some recent applications.
Abstract O. Venjakob:
The quadratic Reciprocity Law for the Legendre or Jacobi-Symbol forms the starting point of all Reciprocity Laws as well as of class field theory. It is closely related to the product formula of the quadratic Hilbert-Symbol over local fields. Various mathematicians have established higher explicit formulae to compute higher Hilbert-Symbols. Analogs were found for formal (Lubin-Tate) groups. Eventually Perrin-Riou has formulated a Reciprocity Law, which allows the explicit computation of local cup product pairings by means of Iwasawa- and p-adic Hodge Theory. In this talk I shall try to give an overview of these topics, at the end I will explain recent developments in this regard.

Arithmetic of critical p-adic L-functions
2024-06-06 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 6: Max Witzelsperger: Secondary p-adic L-functions

Purity for the flat cohomology
2024-06-06 09:15 - 10:45 | Heidelberg, Mathematikon, SR tba
Talk 4: Marius Leonhardt (Universität Heidelberg): Inputs from crystalline and prismatic Dieudonné theory

Chromatic Homotopy Theory
2024-06-04 14:00 - 15:30 | Darmstadt, Room 401, Mainz Room 04-432 and Zoom, Darmstadt and Mainz, Darmstadt and Mainz
Torsten Wedhorn (TU Darmstadt)
Talk 8 – Even periodic cohomology theories
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number

Seminar on Arithmetic Geometry
2024-05-31 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Rizacan Ciloglu (TU Darmstadt): Perverse sheaves on twisted affine flag varieties
Zoom 635 7328 0984, Kenncode: kleinste sechsstellige Primzahl

Isotropic motivic categories
2024-05-31 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Fabio Tanania (TU Darmstadt)
In this talk, I will introduce the isotropic stable motivic homotopy category, which is a stable homotopic version of Vishik’s category of isotropic motives. These are local versions of the classical motivic categories SH(k) and DM(k), obtained roughly speaking by annihilating motives of anisotropic varieties. When the base field k is flexible, then isotropic motivic categories have a lot of remarkable properties. As an example, I will describe the structure of cellular isotropic spectra in terms of well-known objects coming from classical homotopy theory. Then, I will discuss what is known about the non-cellular part of isotropic motivic categories and state some open questions.

Shtukas for reductive groups and global Langlands correspondence after Vincent Lafforgue
2024-05-31 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 6: Oğuz Gezmiş (Universität Heidelberg): Cohomology of moduli of shtukas

The rhizomic topology and tropical abelian varieties
2024-05-28 16:00 - 17:00 | Frankfurt, RM-Str. 6-8, R. 308
Leo Herr (Universität Leiden)
Abstract:
The log etale topology is a natural analogue of the etale topology for log schemes. Unfortunately, very few things satisfy log etale descent — not even vector bundles or the structure sheaf. We introduce a new rhizomic topology that sits in between the usual and log etale topologies and show most things do satisfy rhizomic descent! As a case study, we look at tropical abelian varieties and give some exotic examples.

Chromatic Homotopy Theory
2024-05-28 14:00 - 15:30 | Darmstadt, Room 401, Mainz Room 04-432 and Zoom, Darmstadt and Mainz, Darmstadt and Mainz
Paul Siemon (TU Darmstadt)
Talk 7 – Flat modules over MFG
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number

Seminar on arithemtic geometry
2024-05-24 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Torsten Wedhorn (TU Darmstadt): Moduli of truncated shtukas
Zoom 635 7328 0984, Kenncode: kleinste sechsstellige Primzahl

Shtukas for reductive groups and global Langlands correspondence after Vincent Lafforgue
2024-05-24 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 5: Paul Siemon (TU Darmstadt): Geometric Satake

Anabelian geometry
2024-05-23 14:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
14:00 – 15:15 Talk 2: Benjamin Steklov (Goethe Universität): Tannakian formalism
Coffee break
15:45 – 17:00 Talk 3: Amine Koubaa (Goethe Universität): π1alg(X,x) and its properties

Arithmetic of critical p-adic L-functions
2024-05-23 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 5: Marvin Schneider: Triangulations and abstract construction of p-adic L-functions

Purity for the flat cohomology
2024-05-23 09:15 - 10:45 | Heidelberg, MATHEMATIKON, SR 4, INF 205, Heidelberg, Germany
Talk 2: Katharina Hübner (Goethe-Universität Frankfurt): Tilting and the arc topology

Algebraic geometry of the classical Yang-Baxter equation
2024-05-22 16:00 - 17:30 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Oberseminar Algebra und Geometrie
Igor Burban (Universität Paderborn)
Abstract:
Classical Yang-Baxter equation (CYBE) plays an important role in the modern theory of integrable systems. In a seminal work of Belavin and Drinfeld from the year 1983 it was proven that solutions of CYBE can have one of the following three types: elliptic, trigonometric or rational. Moreover, Belavin and Drinfeld gave a complete classification of all elliptic and trigonometric solutions.
In my talk, I am going to explain a geometric description of solutions of (CYBE). Namely, starting with any geometric datum (E, A), where E is a Weierstraß cubic curve and A a torsion free sheaf of Lie algebras (whose generic fiber is a given complex simple Lie algebra) with vanishing cohomology, one can associate to it in a canonical way a solution of CYBE. It turns out that all solutions of CYBE arise in this way. Moreover, the type of the curve in the datum (E, A) (i.e. smooth/nodal/cuspidal) determines the type of the corresponding solution of CYBE (i.e elliptic/trigonometric/rational).
The developed method will be illustrated by explicit examples. This talk is based on my joint works with Raschid Abedin, Lennart Galinat and Thilo Henrich.

Chromatic Homotopy Theory
2024-05-21 14:00 - 15:30 | Darmstadt, Room 401, Mainz Room 04-432 and Zoom, Darmstadt and Mainz, Darmstadt and Mainz
Jon Miles (Uni Frankfurt)
Talk 6 – The moduli stack of formal groups
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number

Chowla-Selberg phenomenon over function fields
2024-05-21 08:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Fu-Tsun Wei (National Tsing Hua University)
In this talk, I will first determine the algebraic relations among various special gamma values over function fields. The result is based on the intrinsic relations between gamma values in question and periods of CM dual t-motives, which are interpreted in terms of their “distributions”. This enables us to express every “abelian” CM period by a suitable product of special gamma values (up to an algebraic multiple), and derive a Chowla–Selberg-type formula in the function field case.
https://tu-darmstadt.zoom.us/j/68048280736

Seminar on Arithmetic Geometry
2024-05-17 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Nathan Tiggemann (TU Darmstadt)
Zoom 635 7328 0984, Kenncode: kleinste sechsstellige Primzahl

Density of rational points near manifolds
2024-05-17 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Damaris Schindler (Universität Göttingen)
Given a bounded submanifold M in R^n, how many rational points with common bounded denominator are there in a small thickening of M? Under what conditions can we count them asymptotically as the size of the denominator goes to infinity? I will discuss some recent work in this direction and arithmetic applications such as Serre’s dimension growth conjecture as well as applications in Diophantine approximation. For this I’ll focus on joint work with Shuntaro Yamagishi, as well as joint work with Rajula Srivastava and Niclas Technau.
