2024-2026 Talks
Geometric Satake Equivalence (2026 Spring)
Generalizing the classical Satake equivalence, geometrizing it to identify the equivariant perverse sheaves of the affine Grassmannian and representations of the dual groups, using the Tannakian formalism. Using this base, see the paths from geometric Langlands to the categorical Langlands
Relative Langlands Program (2025 Spring)
A recent generalization of classical Langlands duality to the setting of spherical varieties and beyond. Dealing with global conjectures on automorphic periods and values of L-functions, as well as local versions of these conjectures which relate to the work of Gan--Gross--Prasad, Ichino--Ikeda and Lapid--Mao.
Point Counting and Orbital Integral (2024 Fall)
Identifying the value of orbital integrals to the number of rational points of the affine Springer fiber, and using Lefschetz trace formula to calculate the number.
Representation Theory of P-adic Groups (2024 Fall)
Reductive groups over local fields, Bernstein decomposition, Bernstein-Zelevinsky classification, and Bushnell, Kutzko's construction of cuspidal representations.
Understanding Rapoport-Zink Space (2024 Spring)
p-divisible group, Dieudonne module, smooth formal group, (iso)crystals.
Explain Rapoport-Zink space via Drinfeld's upper half space, and explain Kudla-Rapoport's paper.
Introduction to p-adic Hodge Theory (2024 Apr)
Compare three types of cohomologies: etale cohomology, de Rham cohomology, and crystalline cohomology of schemes over a p-adic field.