Research

My research is broadly in arithmetic geometry and number theory. My dissertation focused on the explicit hypergeometric modularity method (EHMM), which provides an explicit model for understanding the modularity of hypergeometric motives. The main thread of my current research remains focused on the arithmetic of hypergeometric motives and their connection to modular forms. My broad long-term research goal is to extend the ideas in my dissertation to automorphic forms of higher rank. I describe some of my ongoing projects in the subpages below.

I am also very interested in related areas of arithmetic geometry, and have joined collaborative projects in adjacent fields on two occasions. These are listed as side projects, though I am very committed to working on both. In particular, I am working very hard on the Locally Symmetric Spaces project, which connects to my broader goal of understanding higher rank automorphic forms in relation to hypergeometric motives.

Finally, I have mentored two undergraduate research projects. Details are given under the teaching and mentoring tab.

Preprints and Papers in Preparation

[5] The Arithmetic of Reducible Rank 2 Hypergeometric Motives over Number Fields I [in preparation]

[4] Lifting Finite Field ETFs to p-adic Fields (Joint with Iris Bashinsky*, Matthew Emmert*, and Cameron Shortt*) [in preparation]

[3] The Explicit Hypergeometric Modularity Method III (Joint with Brian Grove, Ling Long, and Fang-Ting Tu). Preprint, [arXiv:2607.25173]

Published Papers

[2] Modular Forms and Certain 2F1(1) Hypergeometric Series, Proceedings of the American Mathematical Society, Vol. 154, No. 7, July 2026, Pages 2803–2818 https://doi.org/10.1090/proc/17616 [arXiv:2502.08760]

[1] L-values of certain weight 3 Modular Forms and Transformations of Hypergeometric Series, Research in the Mathematical Sciences Vol. 13 No. 5, June 2026 https://link.springer.com/article/10.1007/s40687-026-00639-6 [arXiv:2412.07054 ]

Dissertation

[0] Explicit Modularity of Hypergeometric Motives and L-Values of Modular Forms. PhD Dissertation, Louisiana State University, July 2026

*denotes undergraduate coauthors

Invited Talks

Tulane University Algebra and Combinatorics Seminar, 4/5/2026, 'Hypergeometric Functions and CM Modular Forms'
JHU Junior Number Theory Days, 1/31/2026: 'Hypergeometric Motives and Modular Forms'
LSU Number Theory Seminar, 11/2025: 'Modular Forms and Hypergeometric Series'
AMS Southeastern Sectional Meeting New Orleans, 10/5/2025: 'Hypergeometric Series and CM Modular Forms'
SIAM/CAIMS joint conference, Montreal: 7/2025, 'CM modular forms and hypergeometric series'
AMS Western Sectional Meeting San Luis Obispo, 5/1/2025: 'Certain 2F1(1) Hypergeometric Series and Modular Forms'
Joint Math Meetings, Seattle, 1/9/2025: 'Transcendence of 2F3(1) Hypergeometric Series and L-values of Modular Forms '
SERMON, Wofford College, 4/27/2024: 'Symmetries of Modular Forms and Hypergeometric Functions'
Joint Math Meetings, San Francisco, 1/4/2024: 'Triangle Groups and Hypergeometric Transformations'

Symmetries of hypergeometric series induced from modular forms, described in my paper [1]

Selected conferences/workshops attended

Arizona Winter School on Computational Number Theory, March 2026
Rethinking Number Theory 5, June 2025
Southern Regional Number Theory: 10 year anniversary, LSU, March 2024 (student organizer)
Automorphic Forms Workshop, 2023 and 2026
Roots of Unity Workshop, University of Minnesota, June 2022

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