# Seminars Calendar

**Friday May 12, 2023 - **Francesco Campagna (Leibniz Universität Hannover)

**TBA**

**Friday April 21, 2023 - **Juan Esteban Rodriguez Camargo

**TBA**

**Thursday April 20, 2023 - 14:30 - 2AB40 - Andreas Hochenegger**

**Relations among P-twists**

Abstract: On a K3 surface, rational curves and line bundles give rise to interesting autoequivalences of its derived category, so-called spherical twists. It was shown by P. Seidel and R. Thomas, that these spherical twists are mirror-dual to Dehn twists in symplectic geometry. Moreover, they showed that given a chain of rational curves, the associated spherical twists satisfy braid relations. Generalising from K3 surfaces to hyperkähler varieties, D. Huybrechts and R. Thomas showed that the corresponding generalisation of the spherical twists are P^n-twists. In this talk, I will introduce these autoequivalences, and speak about the possible relations among them. This talk is about joint work with Andreas Krug.

**Friday April 14, 2023 - **Heer Zhao

**Log p-divisible groups and semi-stable Galois representations**

Abstract: Let K be a complete discrete valuation field of mixed characteristic (0,p), let R be the ring of integers of K, and let G be the absolute Galois group of K. A famous conjecture of Fontaine (proved by Fontaine, Laffaille, Breuil, and Kisin) states that an integral p-adic representation of G with Hodge-Tate weights in [0,1] is crystalline iff it arises from a p-divisible group over R. We generalize the above to: an integral p-adic representation of G with Hodge-Tate weights in [0,1] is semi-stable iff it arises from a log p-divisible group over R (endowed with the canonical log structure). This is based on a joint work with Alessandra Bertapelle and Shanwen Wang.

**Friday March 24, 2023 - Alberto Vezzani**

**Motivic monodromy and p-adic cohomology theories**

Abstract: In this talk, we will discuss some recent advances in the theory of motives in the context of rigid analytic geometry. In particular, we offer a new definition of the Hyodo-Kato cohomology, purely defined on the generic fiber, without making any reference to log schemes or the log-de Rham Witt complex. As a consequence, we can construct Clemens-Schmidt-style complexes in the mixed characteristic setting, confirming an expectation of Flach and Morin, and simplify our proof of the p-adic weight monodromy conjecture for smooth projective hypersurfaces. This is a joint work in progress with Federico Binda and Martin Gallauer.

**Tuesday February 14, 2023 - 14:30 - 2AB40 - Robert Cass**

**Geometrization of the mod p Satake isomorphism**

Abstract: The classical Satake isomorphism relates the spherical Hecke algebra of a reductive group G over a local field F to representations of the Langlands dual group. When F is of mixed characteristic (0,p) and the Hecke algebra has characteristic prime to p, the Satake isomorphism has been geometrized by Zhu, Yu, Fargues-Scholze, and Richarz-Scholbach using techniques from p-adic geometry. In this talk, we consider the case where the Hecke algebra has characteristic p. I will speak on my recent joint work with Y. Xu, where we geometrize the mod p Satake isomorphism of Herzig and Henniart-Vignéras using mod p étale sheaves on Witt vector affine flag varieties. Our methods involve the constant term functors inspired from the geometric Langlands program, especially the geometry of certain generalized MirkoviÄ‡-Vilonen cycles. The situation is quite different from l-adic sheaves (l \neq p) because only three of the six functors preserve constructible sheaves.

**Friday February 10, 2023 - 14:30 - 1BC50 - Thibaud van den Hove**

**The integral motivic Satake equivalence**

Abstract: For a reductive group G over a field k, geometric Satake gives an equivalence between the category of equivariant perverse sheaves on the affine Grassmannian of G and the category of representations of the Langlands dual group of G. Depending on the field k, one can use different cohomology theories, such as Betti cohomology, étale cohomology, (arithmetic) D-modules, ... On the other hand, the representation category of the Langlands dual group remains the same, depending only on the coefficients of the cohomology theory. In this talk, I will explain how to construct a version of the Satake equivalence using a universal cohomology theory, i.e., motivically, generalizing most previously known instances of geometric Satake. This is joint work with Robert Cass and Jakob Scholbach.

**Thursday February 2, 2023 - 14:30 - 2AB40 - Alexandr Buryak (Higher School of Economics - Moscow)**

**Counting meromorphic differentials on the Riemann sphere: explicit formulas and a relation with mathematical physics**

Abstract: Counting maps between Riemann surfaces is a classical problem in algebraic geometry and combinatorics, and it was studied for more than one hundred years. In recent years, a related problem of counting meromorphic differentials on Riemann surfaces attracted considerable interest. I will talk about a complete solution of this problem for the Riemann sphere that we obtained recently with Paolo Rossi and will show beautiful explicit formulas that we found.

# Working Seminars

Condensed mathematics 2022

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