Research
Research
My research interests lie at the interface between algebraic topology, quantum algebra, and arithmetic statistics. As a topologist, I like to think about configuration spaces and braid groups, Hurwitz spaces, homological and representation stability, and connections between algebraic topology and other fields. As a number theorist, I am interested in the enumeration of global fields, character sums, multiple Dirichlet series, and L-functions. My current focus includes homological computations of various configuration spaces with twisted coefficients, and their applications to the representation theory of braid groups and problems in number theory such as multiple Dirichlet series and Malle's conjecture for function fields.
An elaborate new proof of Cayley's formula, with Esther Banaian, Elizabeth Kelley, Weston Miller, Jason Stack, Carolyn Stephen, and Nathan Williams. Algebraic Combinatorics 8 (2025), no. 4, pp. 971-995. [arXiv:2402.07798]
Fox-Neuwirth cells, quantum shuffle algebras, and character sums of the resultant. Preprint arXiv:2308.01410 (2023)
Bender-Knuth involutions on linear extensions of posets, with Judy Chiang, Matthew Kendall, Ryan Lynch, Son Nguyen, Benjamin Przybocki, and Janabel Xia. Discrete Mathematics 347 (2024), no. 9, Paper No. 114068, 20 pp. [arXiv:2302.12425]
Fox-Neuwirth cells, quantum shuffle algebras, and the homology of type-B Artin groups. Mathematische Zeitschrift 306 (2024), no. 4, Paper No. 57, 44 pp. [arXiv:2207.12469]
"Hurwitz spaces over punctured curves and Malle's conjecture with local conditions." Available upon request.
"Invariants and coinvariants of braid representations," with Arthur Soulié. Available upon request.
"Unstable homology of generalized Hurwitz spaces and Malle's conjecture for function fields."
"Extensions of braid representations," with Arthur Soulié.
Fox-Neuwirth cells, quantum shuffle algebras, and applications in arithmetic statistics. University of Minnesota Ph.D. dissertation (2024)
Geometry of the Kerr black holes. University of Chicago Mathematics REU expository paper (2017)