# Schedule

## Monday, October 1

 08:30 - 9:30 Registration 09:30 - 10:30 Stephen Kudla: Modular generating series for arithmemic special divisors 10:30 - 11:00 Coffee break (and registration) 11:00 - 12:00 Vincent Pilloni: Hecke operators and the coherent cohomology of Shimura varieties 12:00 - 14:30 Lunch break 14:30 - 15:30 Torsten Wedhorn: The tautological ring for good reductions of Shimura varieties of Hodge type

## Tuesday, October 2

 09:30 - 10:30 Tasho Kaletha 10:30 - 11:00 Coffee break 11:00 - 12:00 Colette Moeglin: Multiplicity in the space of square integrable automorphic forms 12:00 - 15:00 Lunch break 15:00 - 16:00 Ben Howard: Moduli spaces of shtukas and a higher derivate Gross-Kohnen-Zagier formula 16:00 - 16:30 Coffee break 16:30 - 17:30 Wei Zhang: Arithmetic Fundamental Lemma: old and new

## Wednesday, October 3

 09:00 - 10:00 David Hansen: Filtering vector bundles on the Fargues-Fontaine curve, and applications 10:00 - 10:15 Break 10:15 - 11:15 Laurent Fargues 11:15 - 11:45 Coffee break 11:45 - 12:45 Bhargav Bhatt: Prismatic cohomology Free afternoon

## Thursday, October 4

 09:30 - 10:30 Gabriel Dospinescu: On the p-adic étale cohomology of the Drinfeld space 10:30 - 11:00 Coffee break 11:00 - 12:00 Sascha Orlik: On the pro-étale cohomology of Drinfeld´s upper half space 12:00 - 14:00 Lunch break 14:00 - 15:00 Zinwen Zhu 15:00 - 15:15 Short break 15:15 - 16:15 Timo Richarz: Smoothness of Schubert varieties in twisted affine Grassmannians I 16:15 - 16:45 Coffee break 16:45 - 17:45 Tom Haines: Smoothness of Schubert varieties in twisted affine Grassmannians II 19:00 Conference Dinner

## Friday, October 5

 09:30 - 10:30 George Pappas 10:30 - 11:00 Coffee break 11:00 - 12:00 Mark Kisin: Honda-Tate theory for Shimura varieties 12:00 - 14:00 Lunch break 14:00 - 15:00 Xuhua He: $B(G)$ and beyond 15:00 - 15:30 Coffee break 15:30 - 16:30 Eva Viehmann: The Newton poset for some Iwahori double cosets

## Bhargav Bhatt: Prismatic cohomology

I will explain the definition and the basic comparison isomorphisms for prismatic cohomology. As an application, we shall see a new proof of the almost purity theorem that does not involve localizing on (or talking about) adic spaces. Joint work with Peter Scholze.

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## Stephen Kudla: Modular generating series for arithmetic special divisors

In joint work with Jan Bruinier, Ben Howard, Michael Rapoport and Tonghai Yang,

we proved that a certain generating series for the classes of arithmetic divisors on a regular integral model M of a Shimura variety for a unitary group of signature (n-1,1) for an imaginary quadratic field is a modular form of weight n valued in the first arithmetic Chow group of M. I will discuss how this is proved, highlighting the main steps. Key ingredients include information about the divisors of Borcherds forms on the integral model in a neighborhood of the boundary.

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## Vincent Pilloni: Hecke operators and the coherent cohomology of Shimura varieties

We will explain some results towards the construction of Hecke operators on the integral coherent cohomology of Shimura varieties and give arithmetic applications. This is work in progress with Najmuddin Fakhruddin.

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