CRC 326 - GAUS

δ-Forms and Intersection Numbers
2022-05-18 16:00 - 17:00 (Europe/Berlin) | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Oberseminar Algebra und Geometrie
Andreas Mihatsch (Universität Bonn)

Abstract:
δ-Forms were invented by Gubler–Künnemann, they are certain
hybrid objects on non-archimedean spaces that combine the smooth
differential forms of Chambert-Loir–Ducros with tropical intersection
theory. In this talk, I will first present a purely local definition of
δ-forms that is based on the combinatorics of skeletons in Berkovich
spaces. I will then explain an application to intersection numbers on
integral models: The lengths of artinian complete intersections on the
model agree with certain integrals of δ-forms in the generic fiber.

Seminar on étale motives
2022-05-17 14:00 - 15:30 | Darmstadt and Zoom
Talk 5: Interlude on model categories- tba

International Seminar on Automorphic Forms
2022-05-17 09:00 - 10:00 | Zoom
Sato-Tate conjecture in arithmetic progressions for certain families of elliptic curves
In this talk we will study moments of the trace of Frobenius of elliptic curves if the trace is restricted to a fixed arithmetic progression. In conclusion, we will obtain the Sato-Tate distribution for the trace of certain families of Elliptic curves. As a special case we will recover a result of Birch proving Sato-Tate distribution for certain family of elliptic curves. Moreover, we will see that these results follow from asymptotic formulas relating sums and moments of Hurwitz class numbers where the sums are restricted to certain arithmetic progressions. This is a joint work with Kathrin Bringmann and Ben Kane.

Chern-Weil theory and Hilbert-Samuel theorem for semi-positive singular toroidal metrics on line bundles
2022-05-13 16:30 - 17:30 | Frankfurt and Zoom
TGiZ-Seminar: Tropical geometry in Zoom (First meeting Summer Semester 2022)
José Ignacio Burgos Gil (ICMAT, Madrid)
Abstract:
In this talk I will report on joint work with A. Botero, D. Holmes and R. de Jong. Using the theory of b-divisors and non-pluripolar products we show that Chen-Weil theory and a Hilbert Samuel theorem can be extended to a wide class of singular semi-positive metrics. We apply the techniques relating semipositive metrics on line bundles to b-divisors to study the line bundle of Siegel-Jacobi forms with the Peterson metric. On the one hand we prove that the ring of Siegel-Jacobi forms of constant positive relative index is never finitely generated, and we recover a formula of Tai giving the asymptotic growth of the dimension of the spaces of Siegel-Jacobi modular forms.

Toroidal b-divisors and Monge-Ampère measures
2022-05-13 15:00 - 16:00 | Frankfurt and Zoom
TGiZ-Seminar: Tropical geometry in Zoom (First meeting Summer Semester 2022)
Ana María Botero (Regensburg University)
Abstract:
A b-divisor on a smooth projective algebraic variety X is an element in the projective limit of divisors, indexed over all smooth proper modifications of X, and satisfying some functoriality properties. Amongst all b-divisors, the so-called “toroidal” ones can be studied using convex-geometrical and tropical techniques. The aim of the talk is to give an overview of the theory. This joint work with Jose Burgos and Martin Sombra.

Integral models of local Shimura varieties
2022-05-13 14:00 - 15:30 | Darmstadt and Zoom
Abstract: Let $p$ be a prime number. Let $(G, b, mu)$ be a local Shimura datum and $CG$ be a quasi-parahoric group scheme for $G$ (these terms will be explained in the talk). Scholze has defined a functor on the category of perfectoid spaces in characteristic $p$ and has conjectured that this functor is representable by a formal scheme. I will explain the proof of this conjecture for classical groups. The conjecture also gives a group-theoretical interpretation of Rapoport-Zink spaces. This is joint work with G. Pappas.
Meeting-ID: 635 7328 0984
Password: Smallest six digit prime number

Derived $F$-zips
2022-05-12 14:00 - 16:00 | Mainz, Hilbertraum (05-432) and Zoom

Distinguished elements and prisms
2022-05-12 11:15 - 12:15 | Heidelberg, MATHEMATIKON, Hörsaal
GAUS AG: Prismatic Cohomology (Talk 3)
Max Witzelsperger (Heidelberg)

The Logarithmic Hilbert Scheme and its Tropicalisation
2022-05-11 16:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Oberseminar Algebra und Geometrie
Patrick Kennedy-Hunt (University of Cambridge)

Abstract: Let X be a scheme equipped with a SNC divisor D. I will sketch the construction of a proper moduli space of subschemes Z in expansions of X such that Z satisfies an appropriate transversality condition to D. The central insight is a tropical understanding for when Z is flat over the Artin fan of X, and how this behaves in families. I will present the example of the logarithmic linear system, a toric modification of projective space. The associated fan is closely related to the geometry of tropical curves and secondary polytopes. Joint work with Dhruv Ranganathan.

Disputation: Derived F-zips
2022-05-11 15:00 - 16:30 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Can Yaylali

Characterization of Decomposition Groups
2022-05-11 11:30 - 15:45 | Heidelberg, Mathematikon, SR tba
GAUS-AG anabelian geometry on “The Grothendieck conjecture for affine curves”
11:30-13:00: Jakob Stix (Goethe University), talk 3
14:15-15:45: Christian Dahlhausen (Heidelberg University), talk 4

International Seminar on Automorphic Forms
2022-05-10 16:00 - 17:00 | Zoom
A modular construction of unramified p-extensions of Q(N1/p)
In his 1976 proof of the converse of Herbrand’s theorem, Ribet used Eisenstein-cuspidal congruences to produce unramified degree-p extensions of the p-th cyclotomic field when p is an odd prime. After reviewing Ribet’s strategy, we will discuss recent work with Preston Wake in which we apply similar techniques to produce unramified degree-p extensions of Q(N1/p) when N is a prime that is congruent to -1 mod p. This answers a question posed on Frank Calegari’s blog.

Seminar on étale motives
2022-05-10 14:00 - 15:30 | Darmstadt and Zoom
Talk 4: Constructible motives – tba

Explicit geometric Langlands for rigid local systems II
2022-05-06 14:00 - 15:30 | Darmstadt and Zoom
In my second talk I will explain some aspects of the construction of rigid local systems via the geometric Langlands correspondence in more detail. In particular I will focus on joint work with Z. Yun on automorphic data involving euphotic representations, a generalization of J.-K. Yu’s and M. Reeder’s epipelagic representations. Euphotic automorphic data provide a framework for the construction of large classes of rigid local systems. These automorphic data are for example related to generalized hypergeometric sheaves as studied by M. Kamgarpour, L. Yi and D. Xu.

Meeting-ID: 635 7328 0984
Password: Smallest six digit prime number

Moduli spaces in p-adic non-abelian Hodge theory
2022-05-06 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Dr. Ben Heuer, Universität Bonn

Application I: o-minimal Chow.
2022-05-05 16:30 - 17:30 | Darmstadt and Zoom
GAUS AG: The André-Oort conjecture (Talk 4)
Yanik Kleibrink (Goethe University)

o-minimality II: definable cell decomposition.
2022-05-05 15:15 - 16:15 | Darmstadt and Zoom
GAUS AG: The André-Oort conjecture (Talk 3)
Alireza Shavali (Heidelberg University)

Derived completeness
2022-05-05 11:15 - 12:15 | Heidelberg, MATHEMATIKON, Hörsaal
GAUS AG: Prismatic Cohomology (Talk 2)
Rustam Steingart (Heidelberg)

International Seminar on Automorphic Forms
2022-05-03 16:00 - 17:00 | Zoom
We study algebras of modular forms on unitary groups of signature $(n, 1)$. We give a sufficient criterion for the ring of unitary modular forms to be freely generated in terms of the divisor of a modular Jacobian determinant. We use this to prove that a number of rings of unitary modular forms associated to Hermitian lattices over the rings of integers of ${Q}(sqrt{ d})$ for $d = -1, -2, -3$ are polynomial algebras without relations. This is joint work with Haowu Wang.

Seminar on étale motives
2022-05-03 14:00 - 15:30 | Darmstadt and Zoom
Talk 3: The six functors – tba

The geometry of coherent sheaves: From derived categories to Higgs bundles
2022-04-29 14:00 - 17:30 | Frankfurt and Zoom
GAUS-Workshop: “Hodge and Poincaré polynomials of moduli spaces of bundles”
14:00-15:00: Vicente Muñoz (Málaga)
E-Polynomials of the SL(2,C)-character varieties of orientable surfaces
15:15-16:15: Dimitry Wyss (Lausanne)
Intersection cohomology from non-archimedean integrals

Explicit geometric Langlands for rigid local systems I
2022-04-29 14:00 - 15:30 | Darmstadt and Zoom
A local system on a (punctured) curve is called rigid if its isomorphism class is determined by the isomorphism classes of its local monodromy. Perhaps the most famous such local system is the sheaf of solutions to the Gaussian hypergeometric equation. Studying rigidity of this equation dates back to Riemann who used considerations about monodromy to derive quadratic transformations for hypergeometric functions. In this talk I will explain the notion of rigidity for local systems and its role in the geometric Langlands program via rigid automorphic data.
Meeting-ID: 635 7328 0984
Password: Smallest six digit prime number

Recent investigations of L-invariants of modular forms
2022-04-29 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Ass. Prof. Dr. John Bergdall (Bryn Mawr College / MPIM Bonn)

On the motivic cohomology of schemes
2022-04-28 14:00 - 16:00 | Mainz, Hilbertraum (05-432) and Zoom

Delta rings
2022-04-28 11:15 - 12:15 | Heidelberg, MATHEMATIKON, Hörsaal
GAUS AG: Prismatic Cohomology (Talk 1)
Sriram Chinthalagiri Ventaka (Heidelberg)

To infinity and beyond
2022-04-28 09:00 - 09:45 | Heidelberg on ‘Girls’Day 2022 – MINTmachen!
Judith Ludwig (Universität Heidelberg)
The introductory lecture from research will be given by Dr. Judith Ludwig on ‘Girls’Day 2022 – MINTmachen!’ at Heidelberg University.

Generalities on the fundamental groups of curves
2022-04-27 12:15 - 16:00 | Frankfurt (Hörsaal 16)
GAUS-AG anabelian geometry on “The Grothendieck conjecture for affine curves”
12:15-13:45: Pedro Souza (Goethe University), talk 1
14:30-16:00: Marius Leonhardt (Heidelberg University), talk 2

Growth of Bianchi modular forms
2022-04-26 16:00 - 17:00 | Zoom
In this talk, I will establish a sharp bound on the growth of cuspidal Bianchi modular forms. By the Eichler-Shimura isomorphism, we actually give a sharp bound of the second cohomology of a hyperbolic three manifold (Bianchi manifold) with local system arising from the representation Symk⊗Symk¯ of SL2(C). I will explain how a p-adic algebraic method is used for deriving our result.
You can joint the Zoom meeting at https://ethz.zoom.us/j/68930894558
The password is the first Fourier coefficient of the modular j-function (as digits).

Seminar on étale motives
2022-04-26 14:00 - 15:30 | Darmstadt and Zoom
Talk 2: Premotivic categories – tba

Dr. Oliver Bräunling: Hilbert reciprocity using K-theory localization
2022-04-22 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
