CRC 326 - GAUS

Chromatic Homotopy Theory
2024-07-09 14:00 - 15:30 (Europe/Berlin) | Darmstadt, Room 401, Mainz Room 04-432 and Zoom, Darmstadt and Mainz, Darmstadt and Mainz
Thibaud van den Hove (TU Darmstadt)
Talk 13 – The isomorphism between the two towers
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number

Seminar on Arithmetic Geometry
2024-07-05 14:00 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Fabio Tanania (TU Darmstadt): Isotropic motivic fundamental groups
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl

Die absolute Galoisgruppe eines p-adischen Körpers
2024-07-05 13:10 - 14:40 | Heidelberg, Mathematikon, SR A and Livestream
Moshe Jarden (Universität Tel Aviv)
Wir rechnen die Anzahl der Erzeugenden und die Anzahl der Relationen aus, die für die Darstellung der absoluten Galois Gruppen einer gegebenen endlichen Erweiterung von Q_p erforderlich ist.

Shtukas for reductive groups and global Langlands correspondence after Vincent Lafforgue
2024-07-05 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Alireza Shavali (Universität Heidelberg) Talk 11: Moduli of representations and global Langlands parametrization (Part I)

Anabelian geometry
2024-07-04 14:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
14:00 – 15:00 Talk 8: Magnus Carlson (Goethe Universität): Finishing the proof
Coffee break
15:30 – 17:00 Talk 9: Marius Leonhardt (Universität Heidelberg): Frobenius eigenvalues

Purity for the flat cohomology
2024-07-04 09:15 - 10:45 | Heidelberg, Mathematikon, SR tba
Talk 8: Amine Koubaa (Goethe-Universität Frankfurt): The key formula for perfectoid rings

Higher rank Teichmüller spaces, Higgs bundles and magical triples
2024-07-03 16:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Oberseminar Algebra und Geometrie
André Oliveira (Universidade do Porto)
One way to realize Teichmüller space of a closed oriented hyperbolic surface Σ is as the space of discrete and faithful representations π_1(Σ) -> PSL(2,R). These constitute a connected component of the character variety of these representations. Higher rank Teichmüller space is a generalization for higher rank Lie groups. More precisely a higher rank Teichmüller space for a group G is a connected component of the G-character variety of representations π_1(Σ) -> G entirely consisting of discrete and faithful representations.

There are however two important differences comparing to the PSL(2,R)-case. Firstly, such spaces do not exist for any group G, even though their existence has long been established whenever G is a split form (the Hitchin components) or Hermitian (maximal components). Secondly, even if they exist for G, not every discrete and faithful representation in G lies in a higher rank Teichmüller space. It was conjectured by Guichard—Labourie—Wienhard that the representations comprising such spaces are positive representations — a special class of discrete and faithful representations — which only exist when G admits a certain structure called positivity.

Non-abelian Hodge theory yields corresponding connected components of the moduli space M(G) of G-Higgs bundles over an associated compact Riemann surface. We will introduce the notion of magical sl_2-triple and show that a group admits a positive structure if and only if it arises from such a magical triple. Then we we will use these magical triples and Higgs bundles to detect and parameterize components of M(G) which should be higher rank Teichmüller spaces (this was subsequently confirmed by Guichard—Labourie—Wienhard using our work). This is joint work with S. Bradlow, B. Collier, O. García-Prada and P. Gothen.

Spectral decomposition and Siegel-Veech transforms: The case of marked tori
2024-07-02 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Martin Möller (Goethe University Frankfurt)
https://tu-darmstadt.zoom.us/j/68048280736
Abstract: Generalizing the well-known construction of Eisenstein series on the modular curves, Siegel-Veech transforms provide a natural construction of square-integrable functions on strata of differentials on Riemannian surfaces. Even the case of marked tori, a homogeneous space but not for a reductive group provides features that we highlight in this talk with an eye on the general case.

Chromatic Homotopy Theory
2024-07-02 14:00 - 15:30 | Darmstadt, Room 401, Mainz Room 04-432 and Zoom, Darmstadt and Mainz, Darmstadt and Mainz
Timo Richarz (TU Darmstadt)
Talk 12 – Chromatic splitting & vanishing conjectures
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number

Counting congruences between modular forms
2024-06-28 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Jaclyn Lang (Temple University, Philadelphia)
For a given eigenform, how many other eigenforms of the same weight and level are congruent to it modulo a prime l? We will explain how modular representation theory can be used to help answer this question. We focus especially on the case when the level is the square of a prime p such that p = -1 mod l. This is ongoing joint work with Robert Pollack and Preston Wake.

Shtukas for reductive groups and global Langlands correspondence after Vincent Lafforgue
2024-06-28 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Sriram C. Venkata (Universität Heidelberg): Talk 10: Drinfeld’s Lemma

Motivic cohomology of cyclic coverings
2024-06-27 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Tariq Syed (Mainz)
Abstract. The generalized Serre question asks whether algebraic vector bundles over topologically contractible smooth affine complex varieties are always trivial or not. Many examples of topologically contractible smooth affine complex varieties are given by so-called cyclic coverings. In this talk, we present new results on the motivic cohomology of such cyclic coverings which might indicate a positive answer to the generalized Serre question in low dimensions.

Arithmetic of critical p-adic L-functions
2024-06-27 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 9: Otmar Venjakob : Iwasawa theoretic invariants

Purity for the flat cohomology
2024-06-27 09:15 - 10:45 | Heidelberg, Mathematikon, SR tba
Talk 7: Christian Dahlhausen (Universität Heidelberg): Excision for flat cohomology

Symplectic singularities and vertex algebras
2024-06-25 17:00 - 18:00 | Darmstadt, Room S215 401
Tomoyuki Arakawa (RIMS): Symplectic singularities and vertex algebras
Symplectic singularities introduced by Beauville appear in various aspects of representation theory and are referred to as “21st-century Lie theory” by Okounkov. On theother hand, symplectic singularities also arise in the context of quantum field theory in physics, particularly in the Higgs and Coulomb branches of three-dimensional theories, as well as in the Higgs branches of four-dimensional theories.
Additionally, in vertex algebra theory, certain Poisson varieties called associated varieties are defined as geometric invariants, and they often turn out to be symplectic singularities. In such cases, vertex algebras can be regarded as chiral noncommutative deformations of symplectic singularities.
In particular, the 4D/2D duality proposed by Beem et al. in theoretical physics determines vertex algebras as invariants for superconformal four-dimensional theories. It is claimed that the Higgs branch of four-dimensional theories can be reconstructed as the associated variety of vertex algebras. Therefore, all vertex algebras arising from four-dimensional theories are supposed to be chiral noncommutative deformations of singular symplectic varieties.
In this lecture, we will discuss such vertex algebras and their representation theory.

Salem numbers and short geodesics
2024-06-25 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Lola Thompson (Utrecht University): Salem numbers and short geodesics
We will discuss how Mahler measure and related concepts (e.g., Salem numbers) are connected to problems about lengths of geodesics on arithmetic hyperbolic manifolds. As a result, by solving problems using tools from number theory, we are able to answer quantitative questions in spectral geometry. This talk will build towards two goals: showing that short geodesics on arithmetic hyperbolic surfaces are rare, and showing that, on average, geodesic lengths of non-compact arithmetic hyperbolic orbifolds appear with high multiplicity. This talk is based on joint work with Mikhail Belolipetsky, Matilde Lalín, and Plinio G. P. Murillo; and with Benjamin Linowitz, D. B. McReynolds, and Paul Pollack.
https://tu-darmstadt.zoom.us/j/68048280736

Chromatic Homotopy Theory
2024-06-25 14:00 - 15:30 | Darmstadt, Room 401, Mainz Room 04-432 and Zoom, Darmstadt and Mainz, Darmstadt and Mainz
Rizacan Ciloglu (TU Darmstadt)
Talk 11 – Thick subcategories of finite p-local spectra
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number

Seminar on Arithmetic Geometry
2024-06-21 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Michael Rapoport (Universität Bonn): Integral models of Hecke operators
I will discuss the construction of integral models of Hecke correspondences and the extension of Hecke correspondences on automorphic vector bundles to integral models.
Zoom 635 7328 0984, Kenncode: kleinste sechsstellige Primzahl

A local model for potentially Barsotti–Tate Galois representations
2024-06-21 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Stefano Morra (Université Paris 8, St. Denis):
Potentially Barsotti–Tate deformations are an essential tool to achieve arithmetic results as the proof of the Shimura–Taniyama–Weyl conjecture, or the Breuil–M´ezard conjecture. Nevertheless, their geometry is still poorly understood, as such rings showed a rich range of complicated behavior, e.g. they may fail to be normal or regular (as shown in some examples and conjectures by Caruso–David–Mézard). In this talk we will discuss how moduli stack of Breuil–Kisin modules can be used to describe the geometry of moduli of tamely potentially Barsotti–Tate Galois representations (in rank 2 and over an unramified extension of Qp), using the theory of local models of loop groups in mixed characteristic. The main technical tool is an analysis of the p-torsion of a tangent complex to lift affine open charts for scheme–theoretic images between moduli of Breuil–Kisin modules and moduli of Galois representations. As a byproduct, we obtain an algorithmic procedure to compute explicit presentations for any tamely potentially Barsotti–Tate deformation ring for 2-dimensional Galois representations of unramified extensions of Qp.
This is joint work with B. Le Hung and A. Mézard.

Shtukas for reductive groups and global Langlands correspondence after Vincent Lafforgue
2024-06-21 09:00 - 11:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 9: Theresa Kaiser: Specialization to the diagonal (Part II)

F-modules for rings with FFRT, and applications to local cohomology
2024-06-20 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Eamon Quinlan-Gallego (Utah)
Abstract: For a regular ring R of positive characteristic, an F-module over R is an R-module equipped with an “action of Frobenius”. The theory of these F-modules has been used successfully in establishing finiteness properties of local cohomology, and in this talk I will present an extension to the case where R is allowed to have mild singularities (known as finite F-representation type, or FFRT for short). I will then illustrate how this theory can be used to extend previous results on local cohomology to the FFRT case.

Anabelian geometry
2024-06-20 14:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
14:00 – 15:00 Talk 6: Jon Miles (Goethe Universität): Artin motives and H 1
Coffee break
15:30 – 17:00 Talk 7: Jakob Stix (Goethe Universität): Dual representations and Hodge-Tate characters

Arithmetic of critical p-adic L-functions
2024-06-20 11:00 - 13:00 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 8: Arithmetic construction of p-adic L-functions on the eigencurve (Reading session)

Purity for the flat cohomology
2024-06-20 09:15 - 10:45 | Heidelberg, Mathematikon, SR tba
Talk 6: Tim Holzschuh (Universität Heidelberg): Introduction to animated rings and cohomology of affine smooth groups (Part 2)

Heptagons, quartics and theta characteristics
2024-06-19 16:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Oberseminar Algebra und Geometrie
Daniele Agostini (Universität Tübingen)
Abstract: A construction of Wachspress associates to a heptagon a plane quartic curve. This has been recently reinterpreted from the point of view of positive geometry, and numerical computations suggest that a general plane quartic arises from precisely 864 heptagons. We prove this rigorously, via theta characteristics and the finite group PSL(2,7). This is joint work with Daniel Plaumann, Rainer Sinn and Jannik Weisner.

On recent progress on the chiral de Rham complex and modular forms
2024-06-18 17:00 - 18:00 | Darmstadt, Room S215 401
Xuanzhong Dai (RIMS): On recent progress on the chiral de Rham complex and modular forms
The Chiral de Rham complex introduced by Malikov et al. is a sheaf construction of vertex algebras on any smooth manifold or nonsingular algebraic variety. Applying this technique to the upper half plane, we obtain a quantization of modular forms, which recovers the Rankin-Cohen brackets, a family of bilinear operations on modular forms. It has long been speculated that the Rankin-Cohen brackets are connected to vertex operator algebras, as initially proposed by W. Eholzer, Y. Manin, and D. Zagier. Our construction naturally inherits a vertex algebra structure, with the vertex operation fully determined by a slight modification of the Rankin-Cohen brackets.

The fiber bundle method applied to triple product L-functions
2024-06-18 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Miao Gu (University of Michigan): The fiber bundle method applied to triple product L-functions
The Poisson summation conjecture of Braverman-Kazhdan, L. Lafforgue, Ngô, and Sakellaridis predicts that spherical varieties (or Whittaker induction thereof) over a global field admit a theory of Fourier analysis, including a generalized Poisson summation formula. The fiber bundle method is a technique for proving the Poisson summation conjecture for spherical varieties that can be written as a family of simpler spherical varieties for which the Poisson summation conjecture is known. In this talk, I will first explain how to relate a generalized Whittaker induction to triple product L-functions. Then I will explain the fiber bundle method and describe an approach to applying it to prove the expected analytic properties of the triple product L-functions. This is joint work with Jayce Getz, Chun-Hsien Hsu, and Spencer Leslie.
https://tu-darmstadt.zoom.us/j/68048280736

Chromatic Homotopy Theory
2024-06-18 14:00 - 15:30 | Darmstadt, Room 401, Mainz Room 04-432 and Zoom, Darmstadt and Mainz, Darmstadt and Mainz
Chirantan Chowdhury (TU Darmstadt)
Talk 10 – Morava E-theory & Morava K-theory
Zoom meeting ID: 612 2072 7363, Password: [REDACTED] six digit prime number

Junior AG
2024-06-17 | Darmstadt
CM Cycles on GSpin Shimura Varieties
For further details see Programme.

Counting Weierstrass points on degenerating algebraic curves
2024-06-14 16:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Summer Semester 2024)
Lucas Gierczak (Institut Polytechnique de Paris)
Abstract:
Weierstrass points on algebraic curves are special points of high importance in algebraic geometry and arithmetic geometry. In this talk, we study how those special points behave when the algebraic curve degenerates to a nodal curve. To this end, we first explain why tropical geometry is a relevant formalism for studying degeneration questions. We then define a tropical analogue on metric graphs (seen as tropical curves) for Weierstrass points, and explore the properties of the so-called “tropical Weierstrass locus”. We also associate intrinsic weights to the connected components of this locus, and show that their total sum for a given metric graph and divisor is a function of few combinatorial parameters (degree and rank of the divisor, genus of the metric graph). Finally, in the case the divisor on the metric graph comes from the tropicalization of a divisor on an algebraic curve, we specify the compatibility between the Weierstrass loci.
