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# Geometric Methods in Rep Theory Seminar – Jianqiao Xia (Harvard)

## November 20 @ 4:30 pm - 5:30 pm

**Title: Equivalence of Hecke Categories with Deeper Level Structures**

**Abstract:** Inspired by the theory of positive depth representations of p-adic reductive groups, we study Hecke categories associated to certain open compact subgroups smaller than the Iwahori subgroup. In this talk, I will prove that in some cases these Hecke categories are monoidally equivalent to depth 0 Hecke categories of smaller groups. On the function level, our result recovers a family of Hecke algebra isomorphisms already proven by Ju-Lee Kim. The categorical equivalences should be an important ingredient of the local Geometric Langlands conjecture.