Ling Long

Professor

Fellow of American Mathematical Society, Class of 2023

Ph.D. Pennsylvania State University, 2002

Contact: 256 Lockett Hall,  llongATlsu.edu

Teaching

• (Fall 2024) Math4200 Abstract Algebra I
• (Spring 2024) Math 7211 (Graduate) Abstract Algebra II
• (Fall 2023) Math1551 Section 1
• (Fall 2022) Math1550 Sections 12 and 15
  
• (Spring 2022) Math 4201 (Undergraduate) Abstract Algebra II and Math 7211 (Graduate) Abstract Algebra II
• (Fall 2021) Math1553, Honor Cal II
• (Spring 2021) Math7230, Algebraic Number Theory
• (Fall 2019) Math2090 Section 2 and Section 3
• (Spring 2019) Math7230 (Number Theory Jointly with Prof. Hoffman), and Math 2090, Section 2
• (Fall 2018) Math1552, Section 1
• (Spring 2018) Math2085
• (Fall 2017) Math2058, Section 1; Math7210, Algebra I
• (Fall 2016) Math 2057, Section 2; Math 2058 Section 1; Math7230, Algebraic Number Theory
• (Spring 2016) Math1552, Section 17; Math1553, Section 1
• (Fall 2014) Math1550, Section 26 and Section 30
• (Fall 2013) Math2057, Section 5 and Section 6

Research Interests: Number Theory and Applications My Curriculum Vitae is available here.

Grants and Awards:

• Micheal F. and Roberta Nesbit McDonald Professorship, LSU since Fall 2023
• Undergraduate Teaching Award, College of Science, LSU, 2023
• Simons Foundation Travel, PI 2023-2028
• NSF research grant DMS #1602047, PI, 2016-2021
• 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, 2002

Selected Publications: Google Scholar (Click the full list here. )

• Traces of Hecke Operators via Hypergeometric Character Sums, (with Jerome W. Hoffman, Wen-Ching Winnie Li, and Fang-Ting Tu) arXiv:2408.02918 (2024)
• Hodge numbers of hypergeometric data, (with Yifan Yang), arxiv:2404.02834 (2024).
• The Explicit Hypergeometric-Modularity Method, (with Michael Allen, Brian Grove, and Fang-Ting Tu), arxiv:2404.00711 (2024).
• Hypergeometric functions over finite fields, (with Jenny G. Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu), arxiv:1510.02575 , Mem. Amer. Math. Soc. 280 (2022), no. 1382.
• A Whipple $_7F_6(1)$ formula revisited (with Wen-Ching Winnie Li and Fang-Ting Tu), La Mathematica, article/10.1007/s44007-021-00015-6, arXiv:2103.08858 (2022)
• Supercongruences for rigid hypergeometric Calabi--Yau threefolds (with Fang-Ting Tu, Noriko Yui, Wadim Zudilin), Adv. in Math. 393 Article 108058 (2021), 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. of AMS, 371 (2019), 5341-5377.
• Some supercongruences occurring in truncated hypergeometric series (with Ravi Ramakrishna), arXiv:1403.5232 Adv. in Math., 290, 773-808, 2016
• 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.
• 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.

Some talk videos:

• A Lecture Series on Hypergeometric Functions, University of Connecticut, 2021
• A Whipple formula revisited, Seminar at Vanderbilt, 2021

Conference co-Organizer:

• Southern Regional Number Theory Conference, LSU, March 9-11, 2024.
• Southern Regional Number Theory Conference, LSU, March 11-12, 2023.
• Southern Regional Number Theory Conference, LSU, March 12-13, 2022.
• Banff International Research Station (BIRS-IAS) at Hangzhou, China, Modular Forms in Number Theory and Physics (22w5189), October 16-21, 2022 (cancelled).
• Southern Regional Number Theory Confrence, LSU, April 13-14, 2019.
• 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 18-20 2011.
• 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 2008.

Graduate Students:

• Esme Rosen (co-supervised with Fang-Ting Tu, current Ph.D. candidate)
• Paresh Arora (current Ph.D. candidate)
• Brian Grove (co-supervised with Fang-Ting Tu, current Ph.D. candidate)
• Emma Lien (2024 Ph.D. from Louisiana State University)
• Bao Pham (co-supervised with Fang-Ting Tu, 2021 Ph.D. from Louisiana State University)
• Liem Nguyen (2021 Ph.D. from Louisiana State University)
• Christ Kurth (2009 Ph.D. from Iowa State University)
• Joohyung Kim (2005 Ph.D. from Iowa State University, co-major)

Extended visits:

• Max Plank Institute for Mathematics, Bonn Germany, summer 2019
• Hong Kong University, Summer 2017, 2018, 2019, 2023
• Sun Yat-Sen University, Guangzhou, China, summer 2018
• 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:

• International Journal of Number Theory, March 2024-March 2027
  
• Proceedings of the American Mathematical Society, February 2022-January 2026
• Third trimester Proceedings of Triangle groups, Belyi Uniformization and Modularity, Pune India
• The special issue of Journal of Number Theory (Vol 161, April 2016 ) dedicated to Professor Wen-Ching Winnie Li, Journal of Number Theory, April 2016.
• Directions in Number Theory, Conference Proceedings for Women in Numbers 3, Association for Women in Mathematics series, Springer, 2016.
• Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) Special Issue on Modular Forms and String Theory in honor of Noriko Yui, published online in 2018.

Other Educational and Extension Services:

• Mini course "Topics in Number Theory" given at Sun Yat-Sen University in Guangzhou China for advanced undergraduate students.
• Girls Talk Math Podcasts 2018

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• Richard Ng
• Notable Women in Math Playing Cards Mathematicians of EvenQuads Deck 1
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