Department of Mathematics

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 […]