12. April  Yingying Wang  Cohomology of the structure sheaf of DeligneLusztig varieties for GLn. 
19. April  Oliver Bräunling  Hilbert reciprocity using Ktheory localization. The boundary map in Ktheory localization at K_2 is the tame symbol. It sees the tamely ramified part of the Hilbert symbol, but no wild ramification. Gillet has shown how to prove Weil reciprocity using such boundary maps. This implies Hilbert reciprocity for curves over finite fields. However, phrasing Hilbert reciprocity for number fields in a similar way fails because it crucially hinges on wild ramification effects. I will explain how one can solve this problem (except at p=2) by introducing artificial singularities which "fatten up" Ktheory with support in the special point. 
26. April  Yifei Zhao  What is a metaplectic group? The topological group SL_2(R) has a unique double cover up to isomorphism. It is not a linear algebraic group and yet plays a vital role in arithmetics, giving representationtheoretic meaning to modular forms of halfintegral weights. This topological group is an example of a "metaplectic group". In this talk, I will propose a general algebraic framework for such groups over an arbitrary base scheme. They have a combinatorial classification and a notion of duality, extending those of reductive groups. Finally, we will catch a glimpse of Langlands duality for metaplectic groups. 
17. Mai  Hélène Esnault  Recent developments on rigid local systems. We shall review some of the general problems which are unsolved on rigid local systems and arithmetic $\ell$adic local systems. We ‘ll report briefly on a proof (2018 with Michael Gröchenig) of Simpson's integrality conjecture for cohomologically rigid local systems. While all rigid local systems in dimension $1$ are cohomologically rigid (1996, Nick Katz), we did not know until last week of a single example in higher dimension which is rigid but not cohomologically rigid. We’ll present one series of examples (2022, Joint work with Johan de Jong and Michael Gröchenig). 

Marco D'Addezio  Boundedness of the pprimary torsion of the Brauer group of an abelian variety. I will present a new finiteness result for the pprimary torsion of the transcendental Brauer group of abelian varieties defined over finitely generated fields of positive characteristic p. This follows from a certain flat variant of the Tate conjecture for divisors which I formulated and proved for abelian varieties. At the end of the talk, I will also say some words about a second result, related to the main one, about the failure of the surjectivity of the specialisation morphism of the Néron–Severi group in families. More precisely, this theorem says that certain infinitely pdivisible ptorsion classes of the Brauer group of the abelian variety defined over the algebraic closure (which are not in the transcendental Brauer group by the main theorem) provide an obstruction to the surjectivity. 
14. Juni  Vytautas Paškūnas  Deformation Theory of local Galois representations. 
21. Juni  Christophe Spenke  TBA 
28. Juni  Bogdan Zavyalov  TBA 
5. Juli  Damien Junger  TBA 
12. Juli  Mattias Strauch  TBA 