CRC 326 - GAUS

Hodge Witt cohomology with modulus and duality
2023-11-09 14:15 - 15:15 (Europe/Berlin) | Mainz, Hilbertraum 05-432
Kay Rülling (Universität Wuppertal)
Abstract: The theory of cube invariant modulus sheaves developed by Kahn-Miyazaki-Saito-Yamazaki allows to define for any sheaf with transfers and any smooth k-scheme X with effective Cartier divisor D a sheaf whose sections over X can be interpreted as regular sections on the complement of D with pole order at infinity bounded by D. This construction is functorial and has a certain universal property, which makes it hard to compute explicitly. We apply it to the de Rham-Witt sheaves in positive characteristic p and show that in case the support of D has simple normal crossings these sheaves correspond under Grothendieck duality to de Rham Witt sheaves with zeros along D. From this we deduce refined versions of Ekedahl duality, Poincaré duality for crystalline cohomology, and Milne duality for motivic cohomology with p-primary torsion coefficients. This is joint work with Fei Ren.
Zoom Meeting-ID: 967 5163 9626
Passcode: [REDACTED] name of famous mathematician born in Königsberg (small letters)

Linear Relations of 1-Periods
2023-11-08 16:45 - 18:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Frankfurter Seminar – Kolloquium des Instituts für Mathematik
Annette Huber-Klawitter (Universität Freiburg)
Abstract: 1-Periods are complex numbers obtained by integrating an algebraic $1$-form defined over $mathbf{Q}$ (e.g. $dx/x$) over a chain with algebraic end points. The set contains many interesting numbers (e.g., the values of $log$ in algebraic numbers). Their transcendence and the relations between them are a classical question of transcendence theory.
We now have complete picture, explaining the relations qualitatively in terms of obvious relations and also quantitatively, by which we mean dimension formulas.
In the talk we are going to explain some of these general results and then discuss the application to the values of the hypergeometric function–recovering results of Wolfart. (joint work with G. Wüstholz)

Global theta correspondence mod p for unitary groups
2023-11-07 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Xiaoyu Zhang (University Duisburg-Essen)
Theta correspondence is a very important tool in Langlands program. A fundamental problem in theta correspondence is the non-vanishing of the theta lifting of an automorphic representation. In this talk, we would like to consider a mod p version of the non-vanishing problem for global theta correspondence for certain reductive dual pairs of unitary groups. We approach this by looking at the Fourier coefficients of the theta lifting and reduce the problem to the equidistribution of unipotent orbits.
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits).

Around Deligne's companion conjecture
2023-11-06 17:30 - 19:00 | Darmstadt
Zhou Yuenian ((Université Paris Saclay)

Non-archimedean integration on quotients and BPS-invariants
2023-11-03 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Seminar on Arithmetic Geometry
Dimitri Wyss (École Polytechnique Fédérale de Lausanne)
In previous work with F. Carocci and G. Orecchia we discovered that BPS-invariants appearing in Donaldson-Thomas theory for moduli of sheaves on del Pezzo surfaces admit a natural interpretation as non-archimedean integrals. Motivated by this, we develop a non-archimedean integration theory for smooth Artin stacks and obtain as application a new expression of these BPS invariants. In particular this gives a new proof of Maulik-Shen’s $chi$-independence result for del Pezzo surfaces. This is joint work in progress with Michael Groechenig and Paul Ziegler.
Zoom (635 7328 0984, Password: [REDACTED] six digit prime).

Automorphy Lifting with Ĝ-adequate image
2023-11-03 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Dmitri Whitmore (University of Cambridge)
Let F be a number field and G a (split) reductive group. The Langlands program attempts to relate
(1) automorphic representations of G
(2) representations of the absolute Galois group of F valued in Ĝ, the dual group of G.
Automorphy lifting theorems are a way to go from (2) to (1). Such theorems are proved using the Taylor–Wiles method but require certain ‘big image’ hypotheses.
We discuss a generalization of the Taylor–Wiles method. Our generalization results in a weakened big image condition (Ĝ-adequate image), which turns out to hold under certain irreducibility hypotheses. We conclude with applications to modularity of some elliptic curves over quadratic extensions of totally real fields, building on work of Boxer–Calegari–Gee–Pilloni.

Rigid meromorphic cocycles
2023-11-03 09:15 - 10:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Talk 3: Factorization of singular moduli (Sriram Chinthalagiri Venkata)

Rigid Analytic Motives
2023-11-02 15:00 - 16:30 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Talk 3: Algebraic étale motives II
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number.

Exodromy
2023-11-02 12:30 - 14:00 | Mainz, Raum 05-514
Alisa Kannen (Universität Mainz): Stratified spaces

Emerton-Gee-Stacks
2023-11-02 11:00 - 17:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 3: Introduction to Stacks (Gautier Ponsinet)

Arithmeticity of modular forms on G_2
2023-10-31 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Aaron Pollack (University of California San Diego)
Holomorphic modular forms on Hermitian tube domains have a good notion of Fourier expansion and Fourier coefficients. These Fourier coefficients give the holomorphic modular forms an arithmetic structure: there is a basis of the space of holomorphic modular forms for which all Fourier coefficients of all elements of the basis are algebraic numbers. The group G_2 does not have an associated Shimura variety, but nevertheless there is a class of automorphic functions on G_2 which possess a semi-classical Fourier expansion, called the quaternionic modular forms. I will explain the proof that (in even weight at least 6) the cuspidal quaternionic modular forms possess an arithmetic structure, defined in terms of Fourier coefficients.
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits).

Equivariant localization theorems
2023-10-27 15:30 - 17:00 | Zoom
Seminar on Arithmetic Geometry
Charanya Ravi (Indian Statistical Institute, Bangalore Centre)
The classical Atiyah-Bott localization theorem in equivariant singular cohomology is one of the primary computational tools in enumerative geometry when the relevant parameter space has a natural torus action. The theorem asserts that the equivariant cohomology of a space with group action can be recovered, up to inversion of some elements, from the equivariant cohomology of the fixed point subspace. To understand various moduli problems, there is a need to access general parameter spaces (singular and stacky) and to produce refined counts (in different cohomology theories).
This talk will first discuss a unified Atiyah-Bott localization theorem for equivariant Borel-Moore homology theories of algebraic stacks. We will then discuss a categorified version of the result which allows us to deduce the theorem for all oriented theories (cohomology and Borel-Moore homology). The talk is based on joint works with Dhyan Aranha, Adeel Khan, Alyosha Latyntsev, and Hyeonjun Park.
Zoom (635 7328 0984, Password: [REDACTED] six digit prime).

Rigid meromorphic cocycles
2023-10-27 09:15 - 10:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Talk 2: Overview of the theory of complex multiplication

Rigid Analytic Motives
2023-10-26 15:00 - 16:30 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Talk 2: Algebraic étale motives I
• Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number.

Motivic cohomology of mixed characteristic schemes
2023-10-26 14:15 - 15:15 | Mainz, Hilbertraum 05-432
Tess Bouis (Université Paris-Saclay)
Abstract:
I will present a new theory of motivic cohomology for general (qcqs) schemes. It is related to non-connective algebraic K-theory via an Atiyah-Hirzebruch spectral sequence. In particular, it is non-A1-invariant in general, but it recovers classical motivic cohomology on smooth schemes over a Dedekind domain after A1-localisation. The construction relies on the syntomic cohomology of Bhatt-Morrow-Scholze and the cdh-local motivic cohomology of Bachmann-Elmanto-Morrow, and generalises the construction of Elmanto-Morrow in the case of schemes over a field.
Zoom:
Meeting-ID: 967 5163 9626
Passcode: [REDACTED] name of famous mathematician born in Königsberg (small letters)

Exodromy
2023-10-26 12:30 - 14:00 | Mainz, Raum 05-514
Tom Bachmann (Universität Mainz): Introduction

Emerton-Gee-Stacks
2023-10-26 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 2: Alireza Shavali: Moduli of Galois Representations

Various implications of the Nagao-Mestre sum
2023-10-25 16:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Oberseminar Algebra und Geometrie
Seoyoung Kim (Universität Göttingen)
In 1965, Birch and Swinnerton-Dyer formulated a conjecture on the Mordell-Weil rank $r$ of elliptic curves which also implies the convergence of the Nagao-Mestre sum. We show that if the Nagao-Mestre sum converges, then the limit equals $-r+1/2$, and study the connections to the Riemann hypothesis for E. We also relate this to Nagao’s conjecture. Furthermore, we discuss a generalization of the above results for the Selberg classes and hence (conjecturally) for larger classes of $L$-functions.

Siegel modular forms and higher algebraic cycles
2023-10-24 16:00 - 17:00 | Online
International Seminar on Automorphic Forms
Aleksander Horawa (University of Oxford)
Abstract: In recent work with Kartik Prasanna, we propose an explicit relationship between the cohomology of vector bundles on Siegel modular threefolds and higher Chow groups (aka motivic cohomology groups). For Yoshida lifts of Hilbert modular forms, we use a result of Ramakrishnan to prove our conjecture. For Yoshida lifts of Bianchi modular forms, we show that our conjecture implies the conjecture of Prasanna—Venkatesh.
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits).

On a C_2-equivariant Gabber lemma
2023-10-20 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Seminar on Arithmetic Geometry
Tom Bachmann (University of Mainz)
Zoom (635 7328 0984, Password: [REDACTED] six digit prime).

Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations
2023-10-20 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Prof. Dr. Chun Yin Hui (University of Hongkong )
Given a compatible system {rho_lambda : Gal_K to GL_n(E_lambda)}_lambda of semisimple lambda-adic representations of a number field K satisfying mild local conditions, we prove that for almost all lambda any type A irreducible subrepresentation of rho_lambda otimes overline Q_ell is residually irreducible.
We apply this result and some potential automorphy theorem to
prove that rho_ lambda otimes overline Q_ell is residually irreducible for
almost all lambda if the compatible system is attached to a regular algebraic, polarized, cuspidal automorphic representation of GL_n(A_Q) and n leq 6.

Rigid meromorphic cocycles
2023-10-20 09:15 - 10:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Talk 1: Introduction and overview (Judith Ludwig)

Rigid Analytic Motives
2023-10-19 15:00 - 16:30 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Talk 1: Infinity sheaves
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number.

Emerton-Gee-Stacks
2023-10-19 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 1: Marlon Kocher (Universität Heidelberg): Overview

Anabelian geometry
2023-10-18 13:30 - 17:10 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 310, Deutschland
Talk 0: Jakob Stix (Goethe Universität Frankfurt): Overview
Talk 1: Jaro Eichler (Goethe Universität Frankfurt): Stacks
Talk 2: Jaro Eichler (Goethe Universität Frankfurt): Gerbes

Tag der Mathematik
2023-10-10 09:30 - 10:30 | Heidelberg, Pädagogische Hochschule, Hörsaalgebäude, INF 560
Judith Ludwig (Universität Heidelberg): Dobble und die Mathematik

Vector bundles and combinatorial algebraic geometry
2023-10-09 - 2023-10-13 | Frankfurt am Main

Junior Retreat
2023-10-08 - 2023-10-11

Spherical Tropicalization and Berkovich Analytic Groups
2023-10-04 16:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Oberseminar Algebra und Geometrie
Desmond Coles (Univ. of Texas, Austin)
Abstract: Tropicalization is the process by which algebraic varieties are assigned a “combinatorial shadow”. I will review the notion of tropicalization of a toric variety and recent work on extending this to spherical varieties. I will then present how one can construct a deformation retraction from the Berkovich analytification of a spherical variety to its tropicalization.

Conference: Modular Forms and Arithmetic Geometry
2023-09-18 - 2023-09-22 | Darmstadt
