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 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 investigated applications, particularly in random walks and voting theory.
Publications
Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups (with M. Hansen, M. Koyama, M.B.A McDermott, and M.E. Orrison), Journal of Fourier Analysis and Applications (2021)
Inferring Rankings from First Order Marginals, Recent Developments in Mathematical, Statistical and Computational Sciences (2021)
Random walks on the BMW monoid: an algebraic approach, Journal of Algebraic Combinatorics (2019)
Generalized Fourier Transforms and their Applications, dissertation (2015).
Asymptotic Growth of Associated Primes of Certain Graph Ideals, Communications in Algebra 42 (2014)
Awards
Robert C. Good Faculty Fellowship, Spring 2021.
National Science Foundation Graduate Fellowship, 2011-2015.
National Science Foundation GROW with USAID Research and Innovation Fellow, South Africa, Summer 2014.
Selected Presentations and Writings
What I Think About When I Think About Voting, American Mathematical Society Feature Column (2023)
Computational Bounds for Doing Harmonic Analysis on Permutation Modules of Finite Groups, JMM (virtual), April 2022
Your Vote Counts! A talk about using math to analyze election outcomes, Cal State LA Women in Math Seminar (virtual), August 2020
Your Vote Counts! A talk about using math to analyze election outcomes, Kenyon College Math Monday, Gambier, OH, February 2020
Inferring Rankings From First Order Marginals, AMMCS, Waterloo, Ontario, Canada, August 2019