## Research Interests

My research interests lie in 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.

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.

## Papers

Wave Front Sets of Reductive Lie Group Representations IV

Joint with Yoshiki Oshima

In Preparation

Joint with Yoshiki Oshima

In Preparation

Wave Front Sets of Reductive Lie Group Representations III

Joint with Tobias Weich

Advances in Mathematics (313), 2017

Joint with Tobias Weich

Advances in Mathematics (313), 2017

Wave Front Sets of Reductive Lie Group Representations II

Accepted to Transactions of the American Mathematical Society

Accepted to Transactions of the American Mathematical Society

Wave Front Sets of Reductive Lie Group Representations

Joint with Hongyu He and Gestur Olafsson

Duke Mathematical Journal (165), 2016

Joint with Hongyu He and Gestur Olafsson

Duke Mathematical Journal (165), 2016

The Continuous Spectrum in Discrete Series Branching Laws

Joint with Hongyu He and Gestur Olafsson

International Journal of Mathematics (24), 2013

Joint with Hongyu He and Gestur Olafsson

International Journal of Mathematics (24), 2013

Tempered Representations and Nilpotent Orbits

Representation Theory (16), 2012

(Note: An error in the introduction has been corrected in this version. Thank you to Esther Galina and Jorge Vargas.)

Representation Theory (16), 2012

(Note: An error in the introduction has been corrected in this version. Thank you to Esther Galina and Jorge Vargas.)