CRC 326 - GAUS

Conference on A Panorama of Moduli Spaces
2024-02-26 - 2024-03-01 | Frankfurt am Main
https://sites.google.com/view/panoramaofmodulispaces/home

Winter workshop Chabauty--Kim
2024-02-14 08:00 - 2024-02-16 18:00 (Europe/Berlin) | Heidelberg

Motivic tt-geometry
2024-02-09 14:00 - 15:30 | Zoom
Seminar on Arithmetic Geometry
Martin Gallauer (University of Warwick)
Commutative rings are profitably studied from a geometric point of view, giving rise to the field of algebraic geometry. “Categorified commutative rings” (e.g. tt-categories) can similarly be studied geometrically, leading to a field called tt-geometry. I will introduce these ideas and focus on recent progress regarding tt-categories arising in the motivic theory. (Based on joint work with Paul Balmer).
Zoom (635 7328 0984, Password: [REDACTED] six digit prime).

Exodromy
2024-02-09 10:15 - 11:45 | Mainz, Raum 05-514
Marcin Lara (Universität Mainz): Galois categories

Rigid meromorphic cocycles
2024-02-09 09:15 - 10:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Riccardo Zuffetti (TU Darmstadt): Rigid meromorphic cocycles for orthogonal groups II

Rigid Analytic Motives
2024-02-08 15:00 - 16:30 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Talk 13: Jonathan Miles (Goethe University Frankfurt): The Hyodo–Kato cohomology
Talk 14: Thibaud van den Hove (TU Darmstadt): The de Rham–Fargues–Fontaine cohomology
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number.

Emerton-Gee-Stacks
2024-02-08 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 13: Jakob Burgi (Universität Heidelberg): Categorical Langlands

Anabelian geometry
2024-02-07 14:15 - 16:30 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 310, Deutschland
14:15 – 15:15 Talk 13: Magnus Carlsson (Goethe Universität Frankfurt): Birational liftability: reduction to number fields
15:30 – 16:30 Talk 14: Katharina Hübner (Goethe Universität Frankfurt): Birational liftability: proving main theorems

Evaluating the wild Brauer group
2024-02-06 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Rachel Newton (King’s College London)
The local-global approach to the study of rational points on varieties over number fields begins by embedding the set of rational points on a variety X into the set of its adelic points. The Brauer–Manin pairing cuts out a subset of the adelic points, called the Brauer–Manin set, that contains the rational points. If the set of adelic points is non-empty but the Brauer–Manin set is empty then we say there’s a Brauer–Manin obstruction to the existence of rational points on X. Computing the Brauer–Manin pairing involves evaluating elements of the Brauer group of X at local points. If an element of the Brauer group has order coprime to p, then its evaluation at a p-adic point factors via reduction of the point modulo p. For p-torsion elements this is no longer the case: in order to compute the evaluation map one must know the point to a higher p-adic precision. Classifying Brauer group elements according to the precision required to evaluate them at p-adic points gives a filtration which we describe using work of Bloch and Kato. Applications of our work include addressing Swinnerton-Dyer’s question about which places can play a role in the Brauer–Manin obstruction. This is joint work with Martin Bright.
You can join the Zoom meeting at https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits).

Category of matroids with coefficients
2024-02-02 16:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Winter Semester 2023/24)
Manoel Zanoelo Jarra (Universität Groningen)
Abstract: Matroids are combinatorial abstractions of the concept of independence in linear algebra. There is a way back: when representing a matroid over a field we get a linear subspace. Another algebraic object for which we can represent matroids is the semifield of tropical numbers, which gives us valuated matroids. In this talk we introduce Baker-Bowler’s theory of matroids with coefficients, which recovers both classical and valuated matroids, as well linear subspaces, and we show how to give a categorical treatment to these objects that respects matroidal constructions, as minors and duality. This is a joint work with Oliver Lorscheid and Eduardo Vital.

Gluing sheaves along Harder-Narasimhan strata of Bun_2.
2024-02-02 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Seminar on Arithmetic Geometry
Jonathan Miles (University of Frankfurt)
We explain how to glue sheaves on the moduli stack of G-bundles on the Fargues-Fontaine curve. In the case of prime-to-p torsion coefficients, the category D_ét(Bun_G) can be thought of as an approximation of the automorphic data appearing in the geometrization of the local Langlands correspondence due to Fargues-Scholze. The stratification of Bun_G arising from the Harder-Narasimhan slope formalism on G-isocrystals yields a semi-orthogonal decomposition of D_ét(Bun_G) into the derived categories of smooth representations of inner forms of Levi subgroups of G. Between such categories there is a (partial) six functor formalism that can be used to compute how sheaves arising on a quasi-compact open substack interact with sheaves on higher strata via nearby cycles functors, which can be interpreted as a derived analogue of Jacquet restriction functors for parabolic subgroups of G (up to inner twisting). We eventually restrict to G=GL_2 and to sufficiently nice coefficients (notably this includes an algebraic closure of F_ell and Z/ell^n Z for almost all ell prime to p), and we will explain how these computations fundamentally reduce to the étale cohomology of p-adic analogues of locally symmetric spaces, such as the Bruhat-Tits building and moduli spaces of mixed p-adic Hodge structures.
Zoom (635 7328 0984, Password: [REDACTED] six digit prime).

Hard Lefschetz theorem and Hodge-Riemann relations for convex valuations
2024-02-02 14:30 - 15:30 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Winter Semester 2023/24)
Andreas Bernig (Goethe-Universität Frankfurt)
Abstract: The hard Lefschetz theorem and the Hodge-Riemann relations have their origin in the cohomology theory of compact Kähler manifolds. In recent years it has become clear that similar results hold in many different settings, in particular in algebraic geometry and combinatorics (work by Adiprasito, Huh and others). In a recent joint work with Jan Kotrbatý and Thomas Wannerer, we prove the hard Lefschetz theorem and Hodge-Riemann relations for valuations on convex bodies. These results can be translated into an array of quadratic inequalities for mixed volumes of smooth convex bodies, giving a smooth analogue of the quadratic inequalities in McMullen’s polytope algebra. Surprinsingly, these inequalities fail for general convex bodies. Our proof uses elliptic operators and perturbation theory of unbounded operators.

On Voevodsky's reconstruction theorem
2024-02-02 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Sebastian Wolf (Universität 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 how to extend it to certain sufficiently nice singular schemes. If time permits, we will also see what one has to modify to make it work in positive characteristic. This is joint work with Peter Haine.

Exodromy
2024-02-02 10:15 - 11:45 | Mainz, Raum 05-514
Tom Bachmann (Universität Mainz): Spectral higher topoi

Rigid meromorphic cocycles
2024-02-02 09:15 - 10:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Yingkun Li (TU Darmstadt): Rigid meromorphic cocycles for orthogonal groups I

Rigid Analytic Motives
2024-02-01 15:15 - 16:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Meeting ID:612 2072 7363, Password: [REDACTED] six digit prime

Rigid Analytic Motives
2024-02-01 15:00 - 16:30 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Talk 11: Rizacan Ciloglu (TU Darmstadt): Extending realization functors
Talk 12: Torsten Wedhorn (TU Darmstadt): The de Rham realisation functor
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

On the motivic fundamental group
2024-02-01 14:15 - 15:15 | Mainz, Hilbertraum 05-432
Emil Jacobsen (Stockholm)
Abstract: I will introduce the motivic fundamental group of a smooth variety, and explain its relation to the usual fundamental group. The main result can also be phrased as follows: local systems of geometric origin are stable under extension in the category of local systems. I will also present a motivic version of a classical theorem of Hain, on Malcev completions of monodromy representations. At the end, I’ll explain some of the group/representation theoretic tools that go into these result.
Zoom Meeting-ID: 967 5163 9626
Passcode: [REDACTED] name of famous mathematician born in Königsberg (small letters)

Emerton-Gee-Stacks
2024-02-01 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 12: Alireza Shavali (Universität Heidelberg): Crystalline Lifts

Anabelian geometry
2024-01-31 13:15 - 17:00 | Heidelberg, MATHEMATIKON, SR A, Deutschland
13:15 – 14:15 Talk 10: Amine Koubaa (Goethe Universität Frankfurt): SC over fields of finite type: main theorems
14:30 – 15:30 Talk 11: Tim Holzschuh (Universität Heidelberg): Birational liftability: intro
16:00 – 17:00 Talk 12: Leonie Scherer (Goethe Universität Frankfurt): Birational liftability: main tool

Six-dimensional sphere packing and linear programming
2024-01-30 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Matthew de Courcy-Ireland (Stockholm University)
This talk is based on joint work with Maria Dostert and Maryna Viazovska. We prove that the Cohn–Elkies linear programming bound is not sharp for sphere packing in dimension 6. This is in contrast to Viazovska’s sharp bound in dimension 8, even though it is believed that closely related lattices achieve the optimal densities in both dimensions. The proof uses modular forms to construct feasible points in a dual program, generalizing a construction of Cohn and Triantafillou to the case of odd weight and non-trivial Dirichlet character. Non-sharpness of linear programming is demonstrated by comparing this dual bound to a stronger upper bound obtained from semidefinite programming by Cohn, de Laat, and Salmon. Our construction has vanishing Fourier coefficients along an arithmetic progression, which can be explained using skew self-adjointness of Hecke operators.
You can join the Zoom meeting at https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits).

Category of matroids with coefficients
2024-01-26 16:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Winter Semester 2023/24)
Cancelled: postponed to February 02
Manoel Zanoelo Jarra (Universität Groningen)
Abstract: Matroids are combinatorial abstractions of the concept of independence in linear algebra. There is a way back: when representing a matroid over a field we get a linear subspace. Another algebraic object for which we can represent matroids is the semifield of tropical numbers, which gives us valuated matroids. In this talk we introduce Baker-Bowler’s theory of matroids with coefficients, which recovers both classical and valuated matroids, as well linear subspaces, and we show how to give a categorical treatment to these objects that respects matroidal constructions, as minors and duality. This is a joint work with Oliver Lorscheid and Eduardo Vital.

Doing geometry by counting points
2024-01-26 15:30 - 17:00 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Seminar on Arithmetic Geometry
Paul Ziegler (TU Darmstadt)
For a family of polynomials in several variables with integral coefficients, the Weil conjectures give a surprising relationship between the geometry of the complex-valued roots of these polynomials and the number of roots of these polynomials “modulo p”. I will give an introduction to this circle of results and an application motivated by the concept of mirror symmetry from physics.
Zoom (635 7328 0984, Password: [REDACTED] six digit prime).

Hard Lefschetz theorem and Hodge-Riemann relations for convex valuations
2024-01-26 14:30 - 15:30 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Winter Semester 2023/24)
Cancelled: postponed to February 02
Andreas Bernig (Goethe-Universität Frankfurt)
Abstract: The hard Lefschetz theorem and the Hodge-Riemann relations have their origin in the cohomology theory of compact Kähler manifolds. In recent years it has become clear that similar results hold in many different settings, in particular in algebraic geometry and combinatorics (work by Adiprasito, Huh and others). In a recent joint work with Jan Kotrbatý and Thomas Wannerer, we prove the hard Lefschetz theorem and Hodge-Riemann relations for valuations on convex bodies. These results can be translated into an array of quadratic inequalities for mixed volumes of smooth convex bodies, giving a smooth analogue of the quadratic inequalities in McMullen’s polytope algebra. Surprinsingly, these inequalities fail for general convex bodies. Our proof uses elliptic operators and perturbation theory of unbounded operators.

Exodromy
2024-01-26 10:15 - 11:45 | Mainz, Raum 05-514
Alisa Kannen (Universität Mainz): Stratified higher topoi

Rigid meromorphic cocycles
2024-01-26 09:15 - 10:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Oğuz Gezmiş (Universität Heidelberg): The RM values of the Dedekind–Rademacher cocycle

CRC-Colloquium
2024-01-25 17:00 - 18:00 | Mainz, Raum 05-426
15:30 Uhr Ben Heuer (Universität Frankfurt): p-adic non-abelian Hodge theory for non-p-adic mathematicians
16:30 Coffee and Cake
17:00 Uhr Jan Bruinier (TU Darmstadt): Theta functions in geometry and arithmetic
18:30 Uhr: Dinner
Abstract B. Heuer:
In p-adic non-abelian Hodge theory, we study p-adic representations of fundamental groups of projective varieties. This talk will give an introduction to this subject without assuming any background in p-adic geometry. Based on examples, I will explain the “p-adic Simpson correspondence”, with an emphasis on the relation to complex geometry. I will discuss recent advances, the main open questions in the area, and potential applications to complex geometry.
Abstract J. Brunier:
We explain how theta functions can be used to study positive definite quadratic forms and their representation numbers. For indefinite quadratic forms, Kudla and Millson showed that there are analogous theta functions relating the geometry of special cycles on locally symmetric spaces to modular forms. Conjectures of Kudla predict similar results for arithmetic special cycles in Arakelov Chow groups on integral models of orthogonal Shimura varieties. We will also report on some recent results in this context.
Zoom Meeting-ID: 967 5163 9626
Passcode: [REDACTED] name of famous mathematician born in Königsberg (small letters)

Emerton-Gee-Stacks
2024-01-25 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 11: Thibaud van den Hove (TU Darmstadt): Crystalline Stacks

Étale cohomology of the moduli stack of rank 2 vector bundles on the Fargues-Fontaine curve
2024-01-23 14:00 - 15:00 | Frankfurt, Rober-Mayer-Str. 10, Raum 711 klein
Seminar: Non-archimedean geometry
Ruth Wild (Universität Bonn)
Abstract: Motivated by classical calculations, we consider the problem of calculating the etale cohomology of the moduli stack Bun<sub>2</sub> of rank 2 vector bundles on the Fargues-Fontaine curve, as introduced by Fargues and Scholze in their geometrization of the Local Langlands correspondence. We achive this by analyzing a stratafication of this stack and the simple cohomological behavior of the different strata. Along the way, we prove the description of the dualizing sheaf on Bun<sub>2</sub>.

The BZSV duality and the relative Langlands program
2024-01-23 09:00 - 10:00 | Zoom
International Seminar on Automorphic Forms
Wee Teck Gan (National University of Singapore)
I will discuss a duality of Hamiltonian group varieties proposed in a recent preprint of Ben-Zvi, Sakellaridis and Venkatesh, which gives a new paradigm for the relative Langlands program.
I will then discuss a joint work with Bryan Wang on instances of this duality for certain Hamiltonian varieties which quantize to generalized Whittaker models.
You can join the Zoom meeting at https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits).
