Research

My research is mainly in the field of arithmetic geometry and number theory. Some of my work also has a combinatorial flavor, involving graphs or integer partitions. I am interested in exploring more in both the number theoretic directions and the combinatorial directions.

Preprints and Publications:

• Hook Length Biases and General Linear Partition Inequalities. With Cristina Ballantine, Hannah Burson, Amanda Folsom, and Will Craig. Accepted for publication in Research in the Mathematical Sciences, 2023. Preprint available at https://arxiv.org/abs/2303.16512.

• Hook Length Bias in Odd versus Distinct Partitions. With Cristina Ballantine, Hannah Burson, Amanda Folsom, and Will Craig. Accepted for publication in Seminaire Lotharingien de Combinatoire, Proceedings of the 35th International Conference on Formal Power Series and Algebraic Combinatorics, 2023. (PDF, Poster)

• Mock Theta Functions and Related Combinatorics. With Cristina Ballantine, Hannah Burson, Amanda Folsom, Chi-Yun Hsu, and Isabella Negrini. Accepted for publication in Springer Research Directions in Number Theory: Women in  Numbers V.  Association for Women in Mathematics Series, 2023. Preprint available at https://arxiv.org/abs/2202.03329.

• Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6. With Nikola Adžaga, Vishal Arul, Lea Beneish, Mingjie Chen, Shiva Chidambaram, and Timo Keller. Acta Arithmetica, Volume 208, 2023. Preprint available at https://arxiv.org/abs/2105.04811.

(The published version may be slightly different from the arXiv version.) 

• On a Partition Identity of Lehmer. With Cristina Ballantine, Hannah Burson, Amanda Folsom, Chi-Yun Hsu, and Isabella Negrini. Discrete Mathematics, Volume 345, Issue 10, October 2022. Preprint available at https://arxiv.org/abs/2109.00609. 

(The published version may be slightly different from the arXiv version.)

• Harmonic Analysis on Local Systems on Graphs – Towards a Gross-Zagier Formula on CM-cycles over Shimura Curves. Ph.D. Thesis. Available at https://dataspace.princeton.edu/handle/88435/dsp012n49t486r.

(I gave a talk on this work at SLMath, and the video is here.)