peaker: Dr. Pol van Hoften (VU Amsterdam)
Time: 14:00-15:30 January 23, 2024 (Tuesday)
Place: MCM110
Title: Igusa stacks and exotic Hecke correspondences I
Abstract: In this talk I will discuss the conjecture of Liang Xiao and Xinwen Zhu on the existence of exotic Hecke correspondences between the special fibers of different Shimura varieties, and a generalization of their conjecture. I will then discuss my joint work in progress with Jack Sempliner on this generalized conjecture. I will also explain how to reinterpret exotic Hecke correspondences in terms of Igusa stacks.
Speaker: Dr. Pol van Hoften (VU Amsterdam)
Time: 14:00-15:30 January 24, 2024 (Wednesday)
Place: MCM110
Title: Igusa stacks and exotic Hecke correspondences II
Abstract: The goal of this talk is to explain the proof of my joint results in progress with Jack Sempliner on the existence of exotic Hecke correspondences. I will discuss the Piatetski--Shapiro construction, which is a procedure taking a Shimura datum (G,X) and a totally real field F and producing a new Shimura datum (H,Y). I will discuss our joint work identifying (integral models of) Shimura varieties for (G,X) with the fixed point schemes under the action of Gal(F/Q) on integral models of Shimura varieties for (H,Y), and similar results for Igusa stacks. I will then indicate how these results can be applied to prove the existence of exotic Hecke correspondences.
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