## Arithmetic Geometry and Number Theory RTG Seminar: Irreducible components of Affine Deligne-Lusztig varieties.

Seminar | October 14 | 3:10-5 p.m. | 740 Evans Hall

Yihang Zhu, Columbia

Department of Mathematics

The set of irreducible components of an affine Deligne-Lusztig variety is interesting for many applications related to Shimura varieties. A natural symmetry group J acts on this set, and it is desirable to determine the orbits and the stabilizers of this action. In joint work with Rong Zhou, we prove a formula for the number of orbits, earlier conjectured by Miaofen Chen and Xinwen Zhu. In joint work in progress with Xuhua He and Rong Zhou, we show that all the stabilizers are very special parahorics. As an application, we deduce a formula for the number of irreducible components in the basic Newton stratum in Shimura varieties.

In the pre-talk, I will give a crash course on the unramified Hecke algebra and different bases of it.

events@math.berkeley.edu