Date/Time : 08 Sep 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Dai Wenhan, National University of Singapore

Under categorical local Langlands, certain natural coherent sheaves on Vogan stacks give rise to matching automorphic sheaves on Bun_G, which are generally hard to understand. Understanding the stalks of these automorphic sheaves at points of Bun_G would crucially provide a mechanism for the explicit matching of objects along the categorical local Langlands functor. Despite its importance, the general behavior of these stalks remains largely mysterious. In this talk we will study these sheaves for G=GLn at the Vogan stack of the Steinberg parameter. Some recent conjectures predict that at basic points, these stalks are given by generalized Steinberg representations of inner forms of G, up to degree shifts. After formulating the main conjecture, I will report some progress towards its proof in a special case on the degree-zero component of Bun_G, achieved through combinatorial computations inspired by Hansen. If time permits, I will also present an application of the result to cohomology of local Shimura varieties.

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