Title: On the Harish-Chandra regularity theorem Abstract: The Harish-Chandra regularity theorem roughly says that an invariant eigendistribution on a semisimple Lie group is represented by some locally integrable function. We shall explain the proof of this theorem with an emphasis on the case of SL(2).
Title: Exotic spheres from p-adic cohomology theories.Abstract:Part 1: An n-dimensional exotic sphere is a smooth manifold homeomorphic, but not diffeomorphic, to S^n. I will give a leisurely introduction to the telescope conjecture in stable homotopy theory (recently resolved in joint work with Burklund, Levy, and Schlank), by explaining its implications for the diffeomorphism classification of […]
Title: Finiteness for Hecke algebras of p-adic reductive groups. Abstract: Part 1: Let F be a p-adic field, and G the F-points of a reductive group over F. For any compact open subgroup U of F, one can form the Hecke algebra C of complex valued functions on G, invariant under left and right translation by […]
Title: Singularities in Mixed Characteristic via Alterations.Abstract: Multiplier ideals and test ideals are ways to measure singularities in characteristic zero and p > 0 respectively. In characteristic zero, multiplier ideals are computed by a sufficiently large blowup by comparing the canonical module of the base and the resolution. In characteristic p > 0, test ideals were […]
Title: A Geometric Introduction to Representation TheoryAbstract: What exactly does it mean for a group to represent the symmetries of an object? In this talk, I will attempt to answer this question by convincing you that the study of group actions, or representations, comes up even more naturally than the study of groups themselves. We […]
Title: A family of Kahler flying wing steady Ricci solitonsAbstract: Steady Kahler-Ricci solitons are eternal solutions of the Kahler-Ricci flow. I will present new examples of such solitons with strictly positive sectional curvature that live on C^n and provide an answer to an open question of H.-D. Cao in complex dimension n>2. This is joint […]
Title: Syzygies of adjoint linear series on projective varietiesAbstract: Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. Starting with the pioneering work of Mark Green on curves, numerous attempts have been made to extend these results to higher dimensions. Ein and Lazarsfeld proved that if A is a very ample […]
Title: Kloosterman sums in representation theory of GL(n, Fq) Abstract: Given a "nice" irreducible representation of GL(n, Fq), one can define a special matrix coefficient attached to it, called the Bessel function. Often Kloosterman sums show up as special values of these Bessel functions. In this talk, I will first explain my previous results regarding […]
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