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

L-values of certain weight 3 Modular Forms and Transformations of Hypergeometric Series [arXiv:2412.07054 ]
Modular Forms and Certain 2F1(1) Hypergeometric Series, to appear, Proceedings of the American Mathematical Society [arXiv:2502.08760]
'Mixed' CM structures attached to certain hypergeometric representations [in preparation]

Invited Talks

AMS Southeastern Sectional Meeting New Orleans (upcoming)
SIAM/CAIMS joint conference, Montreal: 'CM modular forms and hypergeometric series'
AMS Western Sectional Meeting San Luis Obispo, 5/1/25: 'Certain 2F1(1) Hypergeometric Series and Modular Forms'
Joint Math Meetings, Seattle, 1/9/25: 'Transcendence of 2F3(1) Hypergeometric Series and L-values of Modular Forms '
SERMON, Wofford College, 4/27/24: '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

Contributed Talks

Bayou Arithmetic Research Days (BARDS) 3, LSU, 11/2/23: 'Hypergeometric Transformations arising from Atkin-Lehner Involutions' (lightning talk)
Clifford Lectures, Tulane University, 2/25/24 :'Hypergeometric Transformations arising from Atkin-Lehner Involutions' (lightning talk)
Southern Regional Number Theory Conference, (upcoming): 'Certain 2F1(1) Hypergeometric Series and Modular Forms'

Selected conferences/workshops attended

Rethinking Number Theory 5, June 2025
Southern Regional Number Theory: 10 year anniversary, LSU, March 2024 (student organizer)
Automorphic Forms Workshop, LSU, May 2023
Roots of Unity Workshop, University of Minnesota, June 2022
Pre-Arizona Winter School, Abelian Varieties Course, Online, Fall 2023

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