CRC 326 - GAUS

Category of matroids with coefficients
2024-02-02 16:00 - 17:00 (Europe/Berlin) | 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).

Enumerating motivic nearby cycles
2024-01-19 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Seminar on Arithmetic Geometry
Ran Azouri (Sorbonne Paris North University)
A^1 homotopy theory provides tools to refine geometric invariants on integers to quadratic forms. A key such invariant is the quadratic Euler characteristic; Ayoub’s motivic nearby cycles provide a tool to study singularities in the world of A^1 homotopy.
In the talk I will explain how to compute the quadratic Euler characteristic on the motivic nearby cycles spectrum around certain singularities, using an explicit semistable reduction construction. This, together with a work of Levine, Pepin Lehalleur and Srinivas, adds up to a quadratic conductor formula on schemes with semi-quasihomogeneous singularities, refining formulas of Milnor and Deligne.
Later I will describe how, in a work in progress with Emil Jacobsen, we use a similar semistable reduction argument to compute the motivic monodromy on nearby cycles, generalising to motives the Picard-Lefschetz formula of Deligne and Katz.
Zoom (635 7328 0984, Password: [REDACTED] six digit prime).

Conformal Field Theory
2024-01-19 14:00 - 18:00 | Darmstadt, Room S214/24
14:00-15:00: Britta Spät (University of Wuppertal): On the McKay Conjecture
15:15-16:15: Ida Zadeh (Johannes Gutenberg University Mainz): Mathieu Moonshine and T4/Z3 sigma-models
17:00-18:00: David Reutter (University of Hamburg): A braided tensor 2-category from link homology

Exodromy
2024-01-19 10:15 - 11:45 | Mainz, Raum 05-514
Klaus Mattis (Universität Mainz): Gluing squares

Rigid meromorphic cocycles
2024-01-19 09:15 - 10:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Lucas Gerth (Universität Frankfurt): Diagonal restrictions of p-adic Eisenstein families

Rigid Analytic Motives
2024-01-18 15:00 - 16:30 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Talk 10: Can Yaylali (TU Darmstadt): Weight Structures
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number.

Emerton-Gee-Stacks
2024-01-18 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 10: Annie Littler (Universität Heidelberg): Moduli stacks of (φ, Γ)-modules IV – trianguline rank two case

Automorphism group of Cartan modular curves
2024-01-16 16:00 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
International Seminar on Automorphic Forms
Pietro Mercuri (University of Rome – La Sapienza)
We consider the modular curves associated to a Cartan subgroup of GL(2,Z/nZ) or to a particular class of subgroups of GL(2,Z/nZ) containing the Cartan subgroup as a normal subgroup. We describe the automorphism group of these curves when the level is large enough. If time permits, we give a sketch of the proof.
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits).

Junior Symposium
2024-01-15 | Darmstadt

Equivariant motives and actions of finite reductive groups
2024-01-12 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Can Yaylali (Darmstadt/Paris)
Abstract: A finite reductive group G^F is defined as the fixed points of a reductive group G/F_q under the q-Frobenius endomorphism. Their representations were studied by Deligne-Lusztig and Brokemper gave a description of the G^F-equivariant intersection ring of a point (the ring classifying G^F-invariant cycles). Focusing on the latter, I will give an introduction to (rational) motives with group actions and how this is related to equivariant intersection theory. I will use this formalism to relate motives with G^F-action to equivariant motives on the associated flag variety. I will also explain how this relates to Brokemper’s computations on algebraic cycles. If time permits, I will try to discuss the implications on l-adic cohomology and how this can be used in the future to study motivic representation theory of G^F following Deligne-Lusztig.
