Research
(with Michael Allen, Brian Grove, and Ling Long) The Explicit Hypergeometric-Modularity Method. arXiv: 2404.00711
(with Jerome William Hoffman) QM Abelian Varieties, Hypergeometric Character Sums, and Modular Forms. (Survey, submitted)
(with Jerome William Hoffman) Transformations of Hypergeometric Motives. arXiv: 2003.05031
(with Angelica Babei, Lea Beneish, Manami Roy, Holly Swisher, Bella Tobin) Generalized Ramanujan-Sato Series arising from Modular Forms. Research Directions in Number Theory: Women in Numbers V. (To appear)
(with Wen-Ching Winnie Li, and Ling Long) A Whipple $7F6$ formula revisited. La Matematica 1-51, 2022
(with Ling Long, Noriko Yui and Wadim Zudilin) Supercongruences for Rigid Hypergeometric Calab-Yau Threefolds. To Appear (accepted by Adv. Math, 2021). arXiv: 1705.01663 (numerical computations in SageMath and Database of Hecke eigenforms)
(with Jenny G. Fuselier, Ling Long, Ravi Ramakrishna, Holly Swisher) Hypergeometric Functions over Finite Fields. To Appear (accepted by Memoirs of the AMS, 2019). arXiv: 1510.02575
(with Wen-Ching Winnie Li, and Ling Long) Computing Special L-values of Certain Modular Forms with Complex Multiplication. arXiv: 1803.06072 SIGMA 14 (2018), 090, 32 pages
(with Yifan Yang) Evaluation of Certain Hypergeometric Functions over Finite Fields. eprint arXiv: 1711.05842, SIGMA 14 (2018), 050, 18 pages.
(with Sharon Frechette and Holly Swisher) A Cubic Transformation Formula for Appell-Lauricella Hypergeometric Functions over Finite Fields. arXiv: 1701.04526 Research in Number Theory (2018) 4:27
(with Alyson Deines, Jenny G. Fuselier, Ling Long, and Holly Swisher) Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions. Directions in Number Theory, Proceedings for Women in Numbers 3, AWM series, 125-159. (2016)
(with Alyson Deines, Jenny G. Fuselier, Ling Long, and Holly Swisher) Generalized Legendre Curves and Quaternionic Multiplicati. J. Number Theory, 161 (2016), 175-203
(with Yi-Shuan Lin). Twisted Kloosterman Sums. J. Number Theory 147 (2015), 666–690.
Schwarzian differential equations associated to Shimura curves of genus zero. Pacific J. Math. 269 (2014), no. 2, 453–489.
Grants:
I gratefully acknowledge the NSF, the SLMath, the AWM, and the NSA and the NTF for funding my research/conference endeavors.
I gratefully acknowledge the NSF, the SLMath, the AWM, and the NSA and the NTF for funding my research/conference endeavors.
NSF research grant (DMS #2302531, 2023--2026)
SLMath 2023 Summer Research in Mathematics (6/12-6/23/2023). Group Members: Angelica Babei, Manami Roy, Holly Swisher, and Bella Tobin.
NSF Conference Grant (1951773, $29,931): Southern Regional Number Theory Conference (2020--2022) Co-PI: Ling Long
NSA Conference Grant (H98230-21-1-0005, $11,220): Southern Regional Number Theory Conference (optional year: 2022) Co-PI: Ling Long
AWM-NSF Mathematics Mentoring Travel Grants (4/1/2017-6/30/2018)
Mentor: Wen-Ching Winnie Li
My Math "Family":
Yao-Han Chen, Jia-Wei Guo, Yi-Shuan Lin
Esme Rosen (jointly supervise with Ling Long)
Koustav Mondal (jointly supervise with Gene Kopp)
Brian Grove (jointly supervise with Ling Long)
Shashika Petta Mestrige (co-supervised with Karl Mahlburg , 2021 Ph.D.)
Undergraduate Student: August (Ricky) LeBlanc
