Research Interests

I am particularly excited about exploring the link between algebra and graph theory by translating algebraic problems into combinatorial questions about graphs, and vice versa. My graduate research unites discrete mathematics with representation theory and algebraic combinatorics through a generalization of the classical discrete Fourier transform to finite groups and semisimple algebras. I have developed efficient algorithms to compute generalized Fourier transforms and have also analyzed their applications to random walks. For more details, you can view my research statement here. You can also hear me talk about classical Fourier transforms here (starting around 1:36).  

 

Publications

Generalized Condorcet Winners (with A. Meyers, M. Orrison, J. Townsend, and A. Wu), Social Choice and Welfare 43 (2014), no. 1, 11-27. 

Asymptotic Growth of Associated Primes of Certain Graph Ideals, Communications in Algebra 42 (2014), no. 5, 2114-2125.

Generalized Fourier Transforms and their Applications, dissertation (2015).

Separation of Variables and Computation of Fourier Transforms on Finite Groups, II (with D. Maslen and D. Rockmore), Journal of Fourier Analysis and Applications (2016) 

The Efficient Computation of Fourier Transforms on Semisimple Algebras (with D. Maslen and D. Rockmore), Journal of Fourier Analysis and Applications (2017)

Awards

National Science Foundation Graduate Fellowship, 2011-2015.

National Science Foundation GROW with USAID Research and Innovation Fellow, South Africa, Summer 2014.

Selected Presentations

Fourier Analysis on Groups and Algebras: an Algorithm and a Walk (invited), CU Boulder Algebraic Lie Theory Seminar, Boulder, CO, March 2017

Separation of Variables and the Computation of Fourier Transforms on Finite Groups, II (poster), FPSAC, Vancouver, BC, July 2016

Generalized Fourier Transforms (invited), Sam Houston St. Univ. Colloquium, Huntsville, TX, March 2016

A Random Walk Through Algebra, Denison Scientific Association, Denison University, February 2016

Random Walks on the BMW Monoid: an Algebraic Approach, MSRI/PIMS Summer School in Probability, June 2015