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.)