CRC 326 - GAUS

Hybrid curves and their moduli spaces
2023-07-07 14:00 - 15:00 (Europe/Berlin) | Frankfurt, RM-Str. 6-8, Hilbertraum 302 and Zoom
TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Summer Semester 2023)
Noema Nicolussi (University of Potsdam)
Cancelled

Equivariant birational geometry
2023-07-07 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Yuri Tschinkel (New York University)
I will discuss new invariants in equivariant birational geometry, introduced and studied in joint work with Kontsevich, Pestun, Kresch, and Hassett.

Six functor formalism and Poincaré duality
2023-07-06 09:30 - 11:00 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Gastvortrag: Bogdan Zavyalov

Algebraicity of critical Hecke L-values
2023-07-05 16:00 - 17:00 | Frankfurt, Robert-Mayer-Str. 10, Raum 711 groß
Oberseminar Algebra und Geometrie
Johannes Sprang (Universität Duisburg-Essen)
Abstract: Euler’s beautiful formula on the values of the Riemann zeta function at the positive even integers can be seen as the starting point of the investigation of special values of L-functions. In particular, Euler’s result shows that all critical zeta values are rational up to multiplication with a particular period, here the period is a power of 2πi. Conjecturally this is expected to hold for all critical L-values of motives. In this talk, I will explain a joint result with Guido Kings on the algebraicity of critical Hecke L-values up to explicit periods for totally imaginary fields.

Superconnections, Theta series and period domains
2023-07-05 13:15 - 14:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Green forms and the Siegel–Weil formula
Jan Hendrik Bruinier (TU Darmstadt)
Zoom meeting ID 667 3384 5311
Password in request.

A general view on multiple zeta values, modular forms and related q-series
2023-07-04 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Annika Burmester (Bielefeld University)
Multiple zeta values and modular forms have a deep, partly mysterious, connection. This can be seen in the Broadhurst-Kreimer conjecture, which was made partly explicit by Gangl-Kaneko-Zagier in 2006. Further, multiple zeta values occur in the Fourier expansion of multiple Eisenstein series as computed by Bachmann. We will study this connection in more details on a formal level. This means, we review formal multiple zeta values and then introduce the algebra G^f, which should be seen as a formal version of multiple Eisenstein series, and also multiple q-zeta values and polynomial functions on partitions simultaneously. We will give a surjective algebra morphism from G^f into the algebra of formal multiple zeta values.
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).

Local Weight-Monodromy Conjecture
2023-07-04 14:00 - 16:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 308
Seminar: Non-archimedean geometry
Bogdan Zavyalov
Abstract: Let X be a smooth and proper variety over a local field K. Then the weight-monodromy conjecture predicts that the monodromy and weight filtrations coincide up to a shift. Recently, P. Scholze proved this conjecture for set-theoretic complete intersections inside the projective space using the theory of perfectoid spaces. Alternatively, one can formulate a (local) version of the weight-monodromy conjecture for the nearby cycles. We will give a precise formulation of this conjecture and prove it in some cases following the strategy of Scholze in the global case. This is joint work with David Hansen.

Prismatization
2023-07-03 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Manuel Blickle (Uni Mainz): Nygaard filtered prismatization over a perfect field
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Motivic monodromy and p-adic cohomology theories
2023-06-30 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Martin Gallauer (University of Warwick)
Limit structures in cohomology provide an indispensable tool in the study of varieties in families. This was brought to perfection in complex geometry and attempts have been made to transport it to arithmetic settings. In this talk I will introduce an approach to placing limit structures in all settings on an equal footing. It allows for a sharpening of this tool in p-adic cohomology. (Joint work with Federico Binda and Alberto Vezzani.)

Bridgeland stability conditions and applications
2023-06-29 15:15 - 17:45 | Darmstadt, S2|15, Room 201 and Zoom
Talk 11: M. Möller (GU Frankfurt): The projectivity of the Bridgeland moduli space for K3
Talk 12: Emanuele Marci (Université Paris-Saclay, Orsay): Bridgeland stability conditions on Calabi-Yau manifolds
Abstract:
I will give a short overview on Bridgeland stability conditions on Calabi-Yau manifolds, presenting in particular the case of the quintic threefold (C. Li’s Theorem) with applications and, if time permits, of abelian and hyper-Kähler varieties.

Six functor formalism and Poincaré duality
2023-06-29 09:30 - 11:00 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Talk 6: Lukas Waas (Universität Heidelberg): 6FF: construction via compacti cation

Superconnections, Theta series and period domains
2023-06-28 16:00 - 17:00 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Green Forms for Special Cycles II.
Yingkun Li (TU Darmstadt)
Zoom meeting ID 667 3384 5311
Password on request.

Pell-Abel equations
2023-06-28 14:00 - 16:00 | Frankfurt, Robert-Mayer-Str.10, Raum 404
Quentin Gendron (Universidad Nacional Autónoma de México)

Root Number Correlation Bias of Fourier Coefficients of Modular Forms
2023-06-27 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Nina Zubrilina (Princeton 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).

Geometric arcs and fundamental groups of rigid spaces
2023-06-27 14:00 - 16:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 308
Seminar: Non-archimedean geometry
Marcin Lara
Abstract: We introduce a new category of covering spaces in rigid geometry, called geometric coverings, and show it is classified by a certain topological fundamental group. Geometric coverings generalize the class of étale coverings, introduced by de Jong, and its various natural modifications, and have certain desirable properties that were missing from those older notions: they are étale local and closed under taking infinite disjoint unions. The definition is based on the property of unique lifting of “geometric arcs.” On the way, we answer some questions from the foundational paper of de Jong. This is joint work with Piotr Achinger and Alex Youcis.

Prismatization
2023-06-26 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Thibaud van den Hove (TU Darmstadt): Prismatization in characteristic p
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Tangent spaces in p-adic geometry
2023-06-23 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Sean Howe (University of Utah)
Abstract: In complex geometry, it is an extremely useful fact that universal covers of complex manifolds have tangent spaces and that period maps arising from the cohomology of families of varieties are differentiable. In p-adic geometry, unfortunately, it is known that the covers of rigid analytic varieties trivializing local systems of etale cohomology do not admit a good theory of Kahler differentials. In this talk, we explain how, building from first principles and a single clever idea, one can nonetheless assign tangent spaces to many of the perfectoid spaces and diamonds that arise naturally in the study of rigid analytic varieties and their cohomology and then differentiate period maps. These spaces provide, in particular, a natural conceptual framework for predicting when a diamond is a perfectoid space. In this talk we will focus mostly on examples in the theory of local Shimura varieties and explain the relation to work of Johannson, Ludwig and Hansen on perfectoid quotients of Lubin-Tate space, Ivanov and Weinstein on cohomological smoothness, and Pan and Camargo on geometric Sen theory and sheaves of locally analytic functions. This is joint work with Peter Wear.

Bridgeland stability conditions and applications
2023-06-22 15:15 - 17:45 | Purely Online (Exceptional)
Talk 9: A. Bud (GU Frankfurt): Moduli spaces of Bridgeland semistable objects
Talk 10: J. Chen (GU Frankfurt): The Positivity Lemma

Centers of F-purity and their behavior under finite covers
2023-06-22 14:15 - 15:15 | Mainz, Hilbertraum (05-432)
Javier Carvajal-Rojas (Leuven)
Abstract: Let X be an F -split variety (roughly, a strong form of ordinary log Calabi—Yau variety) and Y /X be a finite cover such that the F -splitting of X lifts to Y . How do the spectra of centers of F -purity (roughly, arithmetically tame log-canonical centers) of Y and X relate to one another? This turns out to be a very tricky question due to wild ramification. An optimal answer would look like Cohen—Seidenberg-type theorems for spectra of centers of F-purity. In this talk, I will report on work in progress with A. Fayolle (U. of Utah) where we address this question.

Superconnections, Theta series and period domains
2023-06-21 13:15 - 14:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Green Forms for Special Cycles I.
Riccardo Zuffetti (TU Darmstadt)
Zoom meeting ID 667 3384 5311
Password on request.

Mixed mock modularity of special divisors
2023-06-20 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
Salim Tayou (Harvard University)
Kudla-Millson and Borcherds have proved some time ago that the generating series of special divisors in orthogonal Shimura varieties are modular forms. In this talk, I will explain an extension of these results to toroidal compactifications where we prove that the generating series is a mixed mock modular form. More precisely, we find an explicit completion using theta series associated to rays in the cone decomposition. The proof relies on intersection theory at the boundary of the Shimura variety. This recovers and refines recent results of Bruinier and Zemel. The result of this talk are joint work with Philip Engel and Francois Greer.
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).

Hodge--Tate crystals and p-adic non-abelian Hodge theory
2023-06-20 14:00 - 16:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 308
Seminar: Non-archimedean geometry
Yu Min
Abstract: The coefficient theory of prismatic cohomology has been investigated a lot recently. For example, Morrow–Tsuji and Tian have discovered the relationship between Hodge–Tate crystals and Higgs bundles (at least in the local case). In this talk, I will briefly talk about how to get a global correspondence between Hodge–Tate crystals and Higgs bundles after inverting p. Then I will discuss what we can say without inverting p in the geometric case (over Oc) (if time permits, also in the arithmetic case (over W(k))). This is joint work with Yupeng Wang.

Prismatization
2023-06-19 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Christopher Lang (TU Darmstadt): The conjugate filtration in characteristic p
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

On the K-theory of Z/p^n
2023-06-16 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Dr. Achim Krause (Universität Heidelberg)
Abstract: Algebraic K-theory is an invariant of rings that is notoriously hard to compute, especially in non-regular situations. For example, Quillen computed the K-theory of finite fields already in 1972, but the case of rings of the form Z/p^n for n>1 has been out of reach until now. In joint work with Antieau and Nikolaus, we apply Prismatic Cohomology to this problem, leading to both a practical algorithm to compute these groups, as well as surprising results on their large-degree behaviour.

Superconnections, Theta series and period domains
2023-06-14 13:15 - 14:45 | Darmstadt, Room 244 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289
Weil Representation and Modularity
Christina Röhrig (TU Darmstadt)
Zoom meeting ID 667 3384 5311
Password on request.

Sen Operators and Lie Algebras arising from Galois Representations over p-adic Varieties
2023-06-13 14:00 - 16:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 308
Seminar: Non-archimedean geometry
Tongmu He
Abstract: Any finite-dimensional p-adic representation of the absolute Galois group of a p-adic local field with imperfect residue field is characterized by its arithmetic and geometric Sen operators defined by Sen and Brinon. We generalize their construction to the fundamental group of a p-adic affine variety with a semi-stable chart, and prove that the module of Sen operators is canonically defined, independently of the choice of the chart. When the representation comes from a Qp-representation of the fundamental group, we relate the infinitesimal action of inertia subgroups with Sen operators, which is a generalization of a result of Sen and Ohkubo. These Sen operators can be extended continuously to certain infinite-dimensional representations. As an application, we prove that the geometric Sen operators annihilate locally analytic vectors, generalizing a result of Pan.

Indefinite Theta Functions: something old, something new
2023-06-13 09:00 - 10:00 | Zoom
International Seminar on Automorphic Forms
Sander Zwegers (University of Cologne)
In this talk we give an overview of the theory of indefinite theta functions and discuss some recent results.
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).

Prismatization
2023-06-12 14:00 - 15:30 | Darmstadt and Mainz and Zoom
Marcin Lara (Uni Frankfurt): Hodge filtered de Rham cohomology of p-adic formal schemes
https://tu-darmstadt.zoom.us/j/62421505417?pwd=[REDACTED]
Meeting-ID: 624 2150 5417
Kenncode: [REDACTED]

Conference on Arithmetic, Birational Geometry, and Moduli Spaces
2023-06-12 - 2023-06-16 | Brown University, Providence, RI, USA

Artin's primitive root conjecture: classically and over Fq[T]
2023-06-06 16:00 - 17:00 | Zoom
International Seminar on Automorphic Forms
In 1927, E. Artin proposed a conjecture for the number of primes p ≤ x, for which g generates (ℤ/pℤ)x. By observing numerical deviations from Artin’s originally predicted asymptotic, Derrick and Emma Lehmer (1957) identified the need for an additional correction factor; leading to a modified conjecture that was eventually proved correct by Hooley (1967), under the assumption of the Generalized Riemann Hypothesis (GRH). In this talk we discuss several variants of Artin’s conjecture: namely an “Artin Twin Primes Conjecture”, as well as an appropriate analogue of Artin’s primitive root conjecture for algebraic function fields.
Ezra Waxman (University of Haifa)
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).
