Publications

Research

My research is in number theory, combinatorics, and representation theory. Much of my work is on topics related to automorphic forms on higher rank groups. I am also interested in partitions and the arithmetic of circle packings.  

Publications

Appeared/To Appear

• Prime and thickened prime components in Apollonian circle packings (with E. Fuchs, P. Harris, C. Hsu, J. Rickards, K. Sanden, D. Schindler, and K. Stange). To Appear: Women in Numbers 6 – Research Directions in Number Theory.

• 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

Expository Writing

• Strung out on Automorphic Forms, AMS Feature Column. 2024.

Pedagogical Articles

• Utilizing a poster project as an assessment in an introductory abstract algebra course (with J. Schaefer). PRIMUS. 2024; 34(4), 392-412.

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.

Poems

• Group Theory for Poets. To Appear: Journal of Humanistic Mathematics.

In Preparation

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