Langlands & ARithmetic GEometry Nearly Every Week
A wide-ranging seminar meeting on Mondays 3-4pm in S17-0405.
Please contact Dave, Ian or Si Ying if you'd like to give a talk!
Talks
August 25 (2pm in S17-0611): Adeel Khan (Academia Sinica)
Title: Perverse pullbacks for (-1)-shifted symplectic fibrations
Abstract: I will discuss a new type of pullback operation on perverse sheaves, which is defined for morphisms of complex algebraic stacks equipped with a certain extra structure, namely that of a so-called relative exact (-1)-shifted symplectic fibration. These perverse pullbacks are closely related to classical operations such as vanishing cycles functors and the Fourier-Sato transform. They also vastly generalize the theory of Donaldson-Thomas invariants of Calabi-Yau threefolds, and we will sketch how they lead to a proof of a conjecture of Joyce about their functoriality. Time permitting, I will attempt to briefly survey some applications of these constructions to topics like cohomological Hall algebras, curve counting on Landau-Ginzburg models, and the period sheaves for Hamiltonian G-spaces conjectured by Ben-Zvi, Sakellaridis, and Venkatesh. This is a report on joint work in progress with Tasuki Kinjo, Hyeonjun Park, and Pavel Safronov.
September 1: Dave
Title: Some computations with categorical local Langlands
Handout with examples
September 8: Dai Wenhan (NUS)
Title: Stalks of automorphic Vogan sheaves for the Steinberg parameter of GLn
Abstract: 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.
Handout
September 29: Yifei Zhao (University of Münster)
Title: On an observation of Weissman
Abstract: Around 10 years ago, Weissman constructed the local Langlands correspondence (LLC) for covers of split tori defined by
Brylinski-Deligne extensions. An intriguing phenomenon is that the LLC
map is not surjective in general. The goal of my talk is to relate
this phenomenon to the existence of "extended pure inner forms" of
covers. This is based on joint work with Luozi Shi.
October 13: Si Ying Lee (NUS)
Title: Stacks of p-isogenies with G-structure
Abstract: I will talk about constructing integral models for Hecke correspondences in both the global and local settings, using the theory of F-gauges. Using these integral models, I will explain how one can construct integral Hecke actions on coherent cohomology for compact abelian type Shimura varieties, proving a conjecture of Fakhruddin-Pilloni. This is joint work in progress with Keerthi Madapusi.
December 8: Yuta Takaya (University of Tokyo)