- Ph.D. Pennsylvania State University, 2002
- Contact: 256 Lockett Hall, (225)-578-1654, llongATlsu.edu
- Research Interests: Number Theory and Applications
- Major Research Grants and
- NSF research grant DMS #1602047, PI, 2016-2019
- NSF conference grant DMS #1642598, PI, 2016-2017
- NSF research grant DMS #1303292, PI, 2013-2016
- NSF conference grant DMS #1363265, PI 2014-2015
- AWM Ruth I. Michler Memorial Prize 2012-2013 winner
- NSF research grant DMS#1001332, PI, 2010-2014
- NSA Young Investigators Grant, PI, 2008-2010
- Clay Mathematical Institute: Liftoff Research Fellowship,
- Selected Publications: Google Scolar (Click here for the full list)
- Supercongruences for rigid hypergeometric Calabi--Yau threefolds (with Fang-Ting Tu, Noriko Yui, Wadim Zudilin), preprint 2017, arXiv:1705.01663
- Potentially $GL_2$-type Galois representations associated to noncongruence modular forms (with Wen-Ching Winnie Li and Tong Liu), arxiv:1609.06414 , Trans. AMS, Doi link
- Hypergeometric functions over finite fields, (with
Jenny G. Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu), arxiv:1510.02575
- Some supercongruences occurring in truncated hypergeometric series (with Ravi Ramakrishna), arXiv:1403.5232 Adv. in Math., 290, 773-808, 2016. DOI: 10.1016/j.aim.2015.11.043,
- Galois representations with quaternion
multiplications associated to noncongruence modular forms, (with A.O.L.
Atkin, Wen-Ching Winnie Li, and Tong Liu), arXiv:1005.4105, Trans. Amer. Math. Soc. 365 (2013), no. 12, 6217–6242.
- On l-adic representations for a space of
noncongruence cuspforms, (with Jerome William Hoffman and Helena
Verrill), Proc. Amer. Math. Soc., 140 (2012), 1569-1584.
- Fourier coefficients of noncongruence cuspforms,
(with Wen-Ching Winnie Li), Bull. London Math. Soc. (2012)
- Hypergeometric evaluation identities and
supercongruences, Pacific J. of Math, 249-2 (2011), 405--418.
- On modular forms for some noncongruence subgroups of
the modular group II, (with Chris Kurth), Bull. London Math. Soc.
(2009), Vol. 41 589-598
- On Atkin and Swinnerton-Dyer congruence relations (2)
(with A.O.L. Atkin and Wenching Winnie Li), Mathematische Annalen, Vol.
340, No.2 (2008) 335-358.
- Conference co-Organizer:
- Southern Regional Number Theory Confrence, LSU, April 8-9, 2017.
- Hypergeometric motives and Calabi–Yau differential equations, 3-week program at MATRIX, Melbourne Australia in January 2017.
- Banff International Research Station (BIRS), Modular Forms in String Theory, cerebrating the work of Prof. Noriko Yui, Sep. 26-30 2016
- Mini-workshops on Alegebraic Varieties, Hypergeometric Series, and Modular Forms, Louisiana State University, Baton Rouge, Louisiana, April 2015
- AMS Special Session on Recent Developments in Algebraic Number Theory, JMM 2015, San Antonio,Texas, January 13, 2015
- Banff International Research Station (BIRS), Women in Numbers
3, April 2014
- Applications of Automorphic Forms in Number Theory and
Combinatorics, cerebrating the work of Prof. Wen-Ching Winnie Li, Louisiana State University, Baton Rouge, Louisiana, April 12-15, 2014
- Special Session at AMS sectional meeting at Iowa city, March
- American Institute for Mathematics (AIM) week long workshop
on noncongruence modular forms and modularity, August 2009.
- Special Session at AMS Joint Meeting at San Diego, January
- Extended visits:
- Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University, Fall 2015, Research Fellow
- Cornell University, 2012-2013, Michler Fellow
- National Center for Theoretical Sciences (NCTS) In Taiwan, summer 2007, 2009, 2011, 2013
- University of California at Santa Cruz, Spring 2010
- Institut des Hautes Études Scientifiques(IHES), Summer 2005
- Institute for Advanced Studies (IAS), 2002-2003, member
- Editorial service, co-editor of:
- Other links: