Research

My research is in arithmetic geometry and number theory, with a focus on hypergeometric functions and their relationship with modular forms. I am especially interested in the geometry underlying hypergeometric functions. My work involves explicit modularity theorems for hypergeometric Galois representations using p-adic techniques, exact special L-values of modular forms in terms of hypergeometric series, and the theory of complex multiplication.

Illustration of the Schwarz map, a fundamental theorem connecting modular forms and hypergeometric functions)

Papers

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]
L-values of certain weight 3 Modular Forms and Transformations of Hypergeometric Series, To appear, Research in the Mathematical Sciences [arXiv:2412.07054 ]
Explicit Modularity for Reducible Rank 2 Hypergeometric Motives over Number Fields [in preparation]

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 arXiv:2412.07054

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
Pre-Arizona Winter School, Abelian Varieties Course, Online, Fall 2023

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