My research interests lie at the interface between algebraic topology 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 number theory. As a number theorist, I am interested in the enumeration of global fields, character sums, and heights on stacks. My current focus includes homological computations of various configuration spaces with twisted coefficients, and their applications to arithmetic statistics problems such as trigonometric sums and Malle’s conjecture for function fields.

1. Fox-Neuwirth cells, quantum shuffle algebras, and character sums of the resultant, preprint: arXiv:2308.01410.

2. Bender-Knuth involutions on linear extensions of posets, with Judy Chiang, Matthew Kendall, Ryan Lynch, Son Nguyen, Benjamin Przybocki, and Janabel Xia, preprint: arXiv:2302.12425.

3. Fox-Neuwirth cells, quantum shuffle algebras, and the homology of type-B Artin groups, preprint: arXiv:2207.12469. To appear in Mathematische Zeitschrift.

1. "Configuration spaces and Malle's conjecture for function fields with prescribed ramification."

2. "Trees from affine braid varieties," with Esther Banaian, Elizabeth Kelley, Carolyn Stephen, Lee Trent, and Nathan Williams.

• Geometry of the Kerr black holes, 2017 University of Chicago Mathematics REU expository paper.