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Benjamin Harris

Visiting Assistant Professor

Benjamin Harris

Educational Background

Ph.D. (2011) Massachusetts Institute of Technology

Website(s)

Departments/Programs

  • Mathematics

Research

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.

Publications

  • 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.