15:20 Coffee (or earlier)
15:30 – 16:30 Timo Richarz (TU Darmstadt): Reduction of Shimura Varieties
16:30 Coffee and Cake
17:15 – 18:15 Jens Eberhardt (Universität Mainz): K-motives and Local Langlands
18:45 Dinner

Abstract – Timo Richarz: Reduction of Shimura Varieties
The general theory of Shimura varieties, first developed by Deligne in the 1970s, extends classical objects such as modular curves, moduli of polarized abelian varieties and Hilbert-Blumenthal varieties. The varieties play a crucial role in the search for higher reciprocity laws within the Langlands program. The arithmetic properties of Shimura varieties, in particular their reduction to positive characteristic, have enabled remarkable advances in arithmetic geometry in recent decades. In this talk, I will give an overview of recent results concerning the geometry of Shimura varieties in their reduction to positive characteristic.

Abstract – Jens Eberhardt: K-motives and Local Langlands
In this talk, we construct a geometric realisation of the category of representations of the affine Hecke algebra. For this, we introduce a formalism of K-theoretic sheaves (called K-motives) on stacks. The affine Hecke algebra arises from the K-theory of the Steinberg stack, and we explain how to “categorify” this using K-motives. Lastly, we discuss applications of K-motives to the local geometric Langlands program.