You are here
Visiting Assistant Professor
Abstract Harmonic Analysis
Fourier analysis decomposes a function of a single real variable into an integral of waves. This decomposition has applications to partial differential equations, probability theory, and engineering. Abstract harmonic analysis allows one to decompose a function on a space X with symmetries G into certain harmonic functions for the action of G on X. For instance, X could be a sphere, a hyperboloid, or the space of all full rank lattices in R^n. Problems in abstract harmonic analysis arise naturally in mathematical physics, analytic number theory, and the spectral theory of differential operators.
- Wave Front Sets of Reductive Lie Group Representations III (joint with T Weich). Advances in Mathematics (313), 2017.
- Wave Front Sets of Reductive Lie Groups Representations (joint with H He and G Olafsson), Duke Mathematical Journal (165), 2016.