Analytische Kohomologie von Lubin – Tate (φ, Γ)-Moduln"
2022-11-11 13:30 - 15:00 (Europe/Berlin) | Heidelberg, Mathematikon, SR A and Livestream
Rustam Steingart (Heidelberg University)

On the Drinfeld's Lemma for the pro-étale fundamental group
2022-11-11 15:30 - 17:00 | Darmstadt, Room S215 401
Seminar on Arithmetic Geometry:
Marcin Lara (Goethe University)
Drinfeld’s Lemma for the étale fundamental group serves as a replacement for the Künneth formula in positive characteristic, that holds even when neither of the varieties is proper. I will report on the progress towards extending this result to the pro-étale fundamental group of Bhatt-Scholze. Note: this is still quite an early stage of the project.

Newton-Okounkov Bodies & Tropical Geometry
2022-11-14 - 2022-11-18 | Frankfurt and Zoom
Workshop on Newton-Okounkov bodies and Tropical Geometry, Nov. 14 – 18
Please see more information and registration on the event website: https://sites.google.com/view/workshop-notrop/

K-theory of the integers and the Kummer-Vandiver conjecture
2022-11-15 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Katharina Hübner (Heidelberg University): Finiteness of the K-theory of the integers

Moduli spaces of cocycles and their quotients
2022-11-15 14:00 - 15:30 | Zoom
Moduli of Langlands parameters
The goal of this talk is to describe moduli spaces of cocycles and their quotients by conjugation actions, 1 which will later be applied to L-parameters. More precisely, cover [DHKM20, §A.1,§A.2]. Then recall some background on GIT quotients, and explain the relation between the GIT quotient and the sheaf quotient of moduli of cocycles [DHKM20, §A.3].
Judith Ludwig (University Heidelberg)
Zoom:
Meeting-ID: 61220727363
Password: [REDACTED] six digit prime

Modularity and automorphy of cycles on Shimura varieties
2022-11-15 16:00 - 17:00 | Zoom
Congling Qiu (Yale University):
Algebraic cycles are central objects in algebraic/arithmetic geometry and problems around them are very difficult. For Shimura varieties modularity of generating series with coefficients being algebraic cycles has been proved useful in the of study of algebraic cycles. A closely related problem is the automorphy of representations spanned by algebraic cycles. I will discuss the history of these problems some progress and applications.
International Seminar on Automorphic Forms
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).

Algebraicity of Higher Green Functions at a CM Point
2022-11-17 14:00 - 16:00 | Mainz, Hilbertraum (05-432)
Yingkun Li (Darmstadt/Mainz)
Abstract: By the classical theory of complex multiplication, the modular j-function takes algebraic values at CM points. It is an interesting question to ask about the algebraic nature of other types of automorphic functions at CM points. For the automorphic Green function at integral parameters, Gross and Zagier conjectured in the 1980s that their valuesat a CM point is essentially the logarithm of an algebraic number. In this talk, we will discuss recent progress toward this conjecture. This is partly joint with Jan Bruinier and Tonghai Yang.

A survey of Galois deformation theory
2022-11-18 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Ravi Ramakrishna (Cornell University)

K-theory of the integers and the Kummer-Vandiver conjecture
2022-11-22 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Tim Holzschuh (Heidelberg University): K-theory and étale cohomology

Buildings
2022-11-22 14:00 - 15:30 | Frankfurt, Robert-Mayer-Str. 10, Raum 110 und Zoom
Jiaming Chen (Goethe University): Group actions and BN pairs

Representatives of L-parameters
2022-11-22 14:00 - 15:30 | Zoom
Moduli of Langlands parameters
Continue the study of moduli of cocycles [DHKM20, §A.4, §A.5, §A.6], and deduce [DHKM20, Theorem 3.1].
Jakob Burgi (Heidelberg University)
Zoom:
Meeting-ID: 61220727363
Password: [REDACTED] six digit prime

Orthogonal modular forms, Siegel modular forms and Eisenstein congruences
2022-11-22 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
The theta correspondence between the orthogonal group and the symplectic group provides a cornerstone for studying Siegel modular forms via orthogonal modular forms. In this work, we make this correspondence completely explicit, with precise level structure for low to moderate even rank and nontrivial discriminant. Guided by computational discoveries, we prove congruences between eigenvalues of classical modular forms and eigenvalues of genuine Siegel modular forms, obtain formulas for the number of neighbors in terms of eigenvalues of classical modular forms, and formulate some conjectures that arise naturally from the data. This is joint work with Dan Fretwell, Colin Ingalls, Adam Logan, Spencer Secord, and John Voight
Eran Assaf (Dartmouth College)
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).

P=W phenomena on singular moduli spaces
2022-11-23 16:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Oberseminar Algebra und Geometrie
Camilla Felisetti (University of Modena)
Abstract:
Irreducible holomorphic symplectic (IHS) varieties can be thought as a generalization of hyperkähler manifolds allowing singularities.
Among them we can find for example moduli spaces of sheaves on K3 and abelian surfaces, which have been recently shown to play a crucial role in non abelian Hodge theory.
After recalling the main features of IHS varieties, I will present several results concerning their intersection cohomology and the perverse filtration associated with a Lagrangian fibration, establishing a compact analogue of the celebrated P=W conjecture by de Cataldo, Hausel and Migliorini for varieties which admit a symplectic resolution.
The talk is based on joint works with Mirko Mauri, Junliang Shen and Qizheng Yin.

Limit periods on curves and arithmetic heights
2022-11-24 14:00 - 16:00 | Mainz, Hilbertraum (05-432)
Emre Sertöz (Hannover)
We show that in a nodal degeneration of smooth curves, the periods of the resulting limit mixed Hodge structure (LMHS) contain arithmetic information. For instance, if the nodal fiber is identified with a smooth curve C glued at two points p and q then the LMHS relates to the Neron–Tate height of p-q in the Jacobian of C. This observation combines an idea resembling “arithmetic deformation to the normal cone” with a study of the divergence behavior of the periods of a degenerating family of curves. Joint work with Robin de Jong and Spencer Bloch.

Non-hypergeometric E-functions
2022-11-24 15:15 - 17:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
15:15-16:15: Rızacan Çiloğlu (TU Darmstadt): Some aspects of differential Galois theory
16:45-17:45: Anton Güthge (TU Darmstadt): Tannakian categories

Homotopy Theory in Condensed Mathematics
2022-11-25 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Catrin Mair (TU Darmstadt)

Quadratically enriched tropical intersections 1
2022-11-25 14:00 - 15:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
TGiZ-Seminar: Tropical geometry in Zoom (First meeting Winter Semester 2022/23)
Sabrina Pauli (Universität Duisburg-Essen)
Abstract:
Tropical geometry has been proven to be a powerful computational tool in enumerative geometry over the complex and real numbers. Results from motivic homotopy theory allow to study questions in enumerative geometry over an arbitrary field k. In these two talks we present one of the first examples of how to use tropical geometry for questions in enuemrative geometry over k, namely a proof of the quadratically enriched Bézout’s theorem for tropical curves.
In the first talk we explain what we mean by the “quadratic enrichment”, that is we define the necessary notions of enumerative geometry over arbitrary fields valued in the Grothendieck-Witt ring of quadratic forms over k.

Isotropic motivic homotopy theory
2022-11-25 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Seminar on Arithmetic Geometry
In this talk I will introduce isotropic motivic homotopy theory, which is a localization of the usual motivic homotopy theory obtained, roughly speaking, by “killing” anisotropic varieties. First, I will present the triangulated category of isotropic motives, constructed by Vishik, as well as its stable homotopic counterpart. Then, I will discuss the structure of the category of isotropic cellular spectra, which are deeply related to comodules over the classical dual Steenrod algebra.
Zoom (Meeting-ID: 635 7328 0984, Password: [REDACTED] six digit prime)
Fabio Tanania, LMU München

Quadratically enriched tropical intersections 2
2022-11-25 15:30 - 16:30 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
TGiZ-Seminar: Tropical geometry in Zoom (First meeting Winter Semester 2022/23)
Andrés Jaramillo Puentes (Universität Duisburg-Essen)
Abstract:
Tropical geometry has been proven to be a powerful computational tool in enumerative geometry over the complex and real numbers. Results from motivic homotopy theory allow to study questions in enumerative geometry over an arbitrary field k. In these two talks we present one of the first examples of how to use tropical geometry for questions in enuemrative geometry over k, namely a proof of the quadratically enriched Bézout’s theorem for tropical curves.
In the second talk we define the quadratically enriched multiplicity at an intersection point of two tropical curves and show that it can be computed combinatorially. We will use this new approach to prove an enriched version of the Bézout theorem and of the Bernstein–Kushnirenko theorem, both for enriched tropical curves.

Valuative invariants for large classes of matroids
2022-11-25 16:45 - 17:45 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
TGiZ-Seminar: Tropical geometry in Zoom (First meeting Winter Semester 2022/23)
Benjamin Schröter (Universität Frankfurt)
Abstract:
Valuations on polytopes are maps that combine the geometry of polytopes with relations in a group. It turns out that many important invariants of matroids are valuative on the collection of matroid base polytopes, e.g., the Tutte polynomial and its specializations or the Hilbert–Poincaré series of the Chow ring of a matroid.
In this talk I will present a framework that allows us to compute such invariants on large classes of matroids, e.g., sparse paving and elementary split matroids, explicitly. The concept of split matroids introduced by Joswig and myself is relatively new. However, this class appears naturally in this context. Moreover, (sparse) paving matroids are split. I will demonstrate the framework by looking at Ehrhart polynomials, relations in Chow rings of combinatorial geometries, and further examples.
This talk is based on the preprint `Valuative invariants for large classes of matroids’ which is joint work with Luis Ferroni.

Vector-valued orthogonal modular forms
2022-11-29 09:00 - 10:00 | Zoom
International Seminar on Automorphic Forms
I will talk about the theory of vector-valued modular forms on domains of type IV, with some emphasis on its algebro-geometric aspects.
Shouhei Ma (Tokyo Institute of Technology)
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).

K-theory of the integers and the Kummer-Vandiver conjecture
2022-11-29 11:15 - 12:45, 2022-12-06 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Max Witzelsperger (Heidelberg University): K-theory of the integers and cyclotomic fields

Buildings
2022-11-29 14:00 - 15:30 | Frankfurt, Robert-Mayer-Str. 10, Raum 110 und Zoom
Alejandro Vargas (Goethe University): Examples of buildings

Reduction to tame parameters
2022-11-29 14:00 - 15:30 | Zoom
Moduli of Langlands parameters
Prove [DHKM20, Theorem 3.4]. State [DHKM20, Theorem 3.12] and, time permitting, explain how one can prove it by modifying the proof of [DHKM20, Theorem 3.4], cf. [DHKM20, Remark 3.9].
Manuel Hoff (University Duisburg-Essen)
Zoom:
Meeting-ID: 61220727363
Password: [REDACTED] six digit prime

Non-hypergeometric E-functions
2022-12-01 15:15 - 17:45 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
15:15-16:15: Manuel Müller (TU Darmstadt): Holonomic D-modules on A1
16:45-17:45: Felix Pennig (TU Darmstadt): Formal meromorphic connections

Bloch-Kato groups, perfectoid fields, and Iwasawa theory
2022-12-02 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Gautier Ponsinet (Université Bordeaux)
The Bloch-Kato Selmer groups associated with a geometric representation of the Galois group of a number field take part in Bloch and Kato's conjecture on the special values of L functions of motives. In Iwasawa theory, we are interested in the structure of these Bloch-Kato Selmer groups over infinite algebraic fields extensions. To do so, we need to study the local Bloch-Kato groups defined via p-adic Hodge theory. In this talk, I will present new results about the local Bloch-Kato groups over perfectoid fields, thereby answering a question by Coates and Greenberg in new cases. These local results allow to describe the Bloch-Kato Selmer groups over many infinite extensions as Selmer groups "à la Greenberg" which are easier to handle. If time allows, I will present immediate consequences of this description in Iwasawa theory.
livestream:
http://129.206.106.240/UzPL29kB/mathematikon-seminarraum.html

Torsors on valuation rings
2022-12-02 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Seminar on Arithmetic Geometry
A conjecture of Grothendieck and Serre states that a torsor under a reductive group over a Noetherian regular scheme X is Zariski locally trivial if it is generically trivial. Recently, this conjecture has seen progress through the work of Fedorov, Panin and Česnavičius. We shall see the historical background of this conjecture, followed by the techniques that go into the proof of the quasi-split case in the analogous situation when X is a smooth scheme over a valuation ring of rank one.
Arnab Kundu (University Paris-Saclay)
Zoom (Meeting-ID: 635 7328 0984, Password: [REDACTED] six digit prime)

Rigidity properties of the cotangent complex
2022-12-02 14:00 - 16:00 | Mainz, Hilbertraum (05-432)
Srikanth Iyengar (Utah)
This talk is about the cotangent complex of a homomorphism of commutative noetherian rings. I will present some new results on this topic, some due to Benjamin Briggs, and others obtained in collaboration with him, that highlight various rigidity properties of the cotangent complex. These are reported in the following article: https://arxiv.org/abs/2010.13314

Arithmetic Quantum Chaos and L-functions
2022-12-06 09:00 - 10:00 | Zoom
International Seminar on Automorphic Forms
In this talk, I will introduce some aspects of the theory of arithmetic quantum chaos, focusing on the quantum unique ergodicity theorem for automorphic forms on the modular surface. Then I will give some results on effective decorrelation of Hecke eigenforms and the cubic moment of Hecke-Maass cusp forms. The proofs are based on the analytic theory of L-functions.
Bingrong Huang (Shandong University)
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).
