Research

My research is in number theory, representation theory, and combinatorics. Current and recent projects involve the following topics: Weyl group multiple Dirichlet series, spectral theory of automorphic forms, Apollonian circle packings, and colored partition diagrams. 

Publications

Appeared/To Appear

• Twisted Weyl group multiple Dirichlet series over the rational function field. Journal of Number Theory. 2023; 253, 337-367.

• An orbit model for the spectra of nilpotent Gelfand pairs (with W. Grodzicki, W. Johnson, G. Ratcliff, A. Romanov, B. Strasser, and B. Wessel). Transformation Groups. 2020; 25: 859-886

• On the p-parts of Weyl group multiple Dirichlet series. Acta Arithmetica. 2017; 179(4): 301-318

• Crystal graphs, character formulas, and the Gindikin-Karpelevich formula for G_2. (with Louis Gaudet and Paul E. Gunnells). Journal of Algebraic Combinatorics. 2015; 41(4): 1089-1102

• Presentations for quaternionic S-unit groups (with T. Chinburg, S. Howe, M. Kosters, B. Singh, M. Stover, P. Ziegler, and Y. Zhang). Experimental Mathematics. 2015; 24(2): 175-182

• Effective congruences for mock theta functions (with Nickolas Andersen, Jeremy Fuller, and Heidi Goodson). Mathematics. 2013; 1(3): 100-110

• The a-numbers of Jacobians of Suzuki curves (with Derek Garton, Beth Malmskog, Rachel Pries, and Colin Weir). Proceedings of the American Mathematical Society. 2013; 141(9): 3019-3028

Submitted

• Poster projects in an abstract algebra course; joint with J. Schaefer

Book Reviews

• The Bookshelf: Trolling Euclid by Tom Wright. Math Horizons. 2017; 25 (2): 22.

• A Gateway to Number Theory: Applying the Power of Algebraic Curves by Keith Kendig. MAA Reviews. August 1, 2022.

In Preparation

• Spectral theory of automorphic forms applied to string scattering amplitudes; joint with Maryam Khaqan, Kim Klinger-Logan and Manish Pandey

• Prime components in Apollonian packings; joint with E. Fuchs, Piper H., C. Hsu, D. Schindler, K. Sanden, K. Stange