Upstart
  • Home
  • Research
  • Teaching
  • Contact
  • Home
  • Research
  • Teaching
  • Contact

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.

Slides

Slides from a presentation at Sphericity 2019, CIRM Luminy

Papers

The Asymptotics of the Support of Plancherel Measure
Joint with Yoshiki Oshima
In Preparation
Irreducible Characters and Semisimple Coadjoint Orbits
Joint with Yoshiki Oshima
arXiv:1710.10190
Wave Front Sets of Reductive Lie Group Representations III
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
Wave Front Sets of Reductive Lie Group Representations
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
Fourier Transforms of Nilpotent Coadjoint Orbits for GL(n,R)
Journal of Lie Theory (22), 2012
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.)
Powered by Create your own unique website with customizable templates.