CURRICULUM VITAE
LING LONG
Higher Education:
Ph.D., Major in Mathematics, Pennsylvania State University, August 2002 Thesis Advisor: Wen-Ching Winnie Li at Pennsylvania State University; Joint Thesis Advisor: Noriko Yui at Queenâ€™s University
B.Sc., Major in Mathematics and Minor in Computer Science and Engineering, Tsinghua University, China, July 1997
Employments:
Iowa State University, Associate Professor, 2009-present
Iowa State University, Assistant Professor, 2003-2009
Institute for Advanced Study, PostDoc. 2002-2003
Research Interests: Number theory, arithmetic geometry, and algebraic geometry
Finite index subgroups of the modular group and their modular forms
Elliptic curves, elliptic surfaces, K3 surfaces
Arithmetic of Calabi-Yau varieties and its applications
Visiting:
Pennsylvania State University, May-June, 2005 and 2006, Supported by AWM-NSF mentoring travel grant
The Institut des Hautes Ã‰tudes Scientifiques in Bures-sur-Yvette (France), July-August, 2005, Partly supported by ISU foreign travel grant.
Taiwan National Center for Theoretic Sciences, May 2007, July 2009
School of Mathematics & System Sciences, ShanDong University, China, June 2007
Morningside Center of Mathematics at Chinese Academy of Sciences, China, July 2007
McGill University, April 2009, March 2010
Pohang Science and Technology Institute, Korea, Dec. 2009
University of California at Santa Cruz, Jan.-June 2010
Publications:
A. Noncongruence modular forms and finite index subgroups of the modular group
Galois representations with quaternion multiplications associated to noncongruence modular forms, (with A.O.L. Atkin, Wen-Ching Winnie Li, and Tong Liu), preprint 2010.
On l-adic representations for a space of noncongruence cuspforms (with Jerome W. Hoffman and Helena Verrill), Proc. Amer. Math. Soc. accepted for publication.
On modular forms for some noncongruence subgroups of PSL_{2}(Z) II (with Chris A. Kurth), Bull. London Math. Soc. (2009), Vol. 41 pp. 589-598.
On modular forms for some noncongruence subgroups of PSL_{2}(Z) (with Chris A. Kurth), Journal of Number Theory, Vol 128 No. 7, (2008) pp 1989-2009.
On Atkin and Swinnerton-Dyer congruence relations (3), Journal of Number Theory, Vol 128 No. 8, (2008) pp2413-2429.
On Atkin and Swinnerton-Dyer congruence relations (2) (with A.O.L. Atkin and Wen-Ching W. Li ), Mathematische Annalen, Volume 340 No. 2 (2008) pp 335-358
On Atkin-Swinnerton-Dyer congruence relations, (with Wen-Ching W. Li and Zifeng Yang), Journal of Number Theory, Volume 113, No. 1 (2005) pp 117-148
Topics Related to Arithmetic Subgroups and Their Modular Forms
B. Classical modular forms, elliptic curves, and related topics
Zeros of some level 2 Eisenstein series (with Sharon Garthwaite, Holly Swisher, Stephanie Treneer), Proc. Amer. Math. Soc. 138 (2010), 467-480.
A short proof of Milne's formulae for sums of integer squares, (with Yifan Yang), International Journal of Number Theory, Volume 1, No. 4, (2005) pp 533-551.
A supercongruence motivated by the Legendre family of elliptic curves, (with Heng-Huat Chang and Wadim Zudilin), Mathematical Notes, Vol. 88, No. 4, pp. 599â€“602, (2010)
A cubic analogue of the Jacobsthal identity, (with Heng-Huat Chang and Yifan Yang), Math Monthly, 118:4 (2010), 316-326.
Hypergeometric evaluation identities and supercongruences, Pacific Journal of Mathematics, 249-2 (2011), 405--418. DOI 10.2140/pjm.2011.249.405
Jacobsthal identity for $\mathbb Q(\sqrt{-2})$, (with Ki-Ichiro Hashimoto and Yifan Yang), Forum Mathematicum, doi:10.1515/FORM.2011.102
C. Elliptic surfaces
On Shioda-Inose structures of one parameter families of K3 surfaces, Journal of Number Theory, Volume 109, No. 2 (2004) pp 299-318
L-series of certain elliptic surfaces, Canadian Mathematical Bulletin, Volume 46, No. 4 (2003), pp. 546-558.
On a Shioda-Inose structure of a family of K3 surfaces, Calabi-Yau Varieties and Mirror Symmetry, Field Institute Communications 38, American Mathematical Society, Providence RI 2003. pp. 201-207
Modularity of Elliptic Surfaces, Ph.D. Dissertation.
D. Algebra and combinatorics
Reciprocity for multirestricted Stirling numbers, joint with Ji Young Choi, Siu-Hung Ng, and Jonathan Smith, Journal of Combinatorial Theory series A, series A, Volume 113 (2006) pp 1050-1060
Catalan loops, (with Jonathan D. H. Smith), Mathematical Proceedings of Cambridge Philosophical Society, Vol. 149, 445-453, (2010)
E. Surveys and expository articles
Zeros of classical Eisenstein series and recent developments, (with Sharon Garthwaite, Holly Swisher, Stephanie Treneer), Fileds Comminucations Volume WIN - Women in Numbers, to appear, survey .
The finite index subgroups of the modular group and their modular forms,Fields institute Communications American Mathematical Society Volume 54, (2008), pp 83-102.
Computations with finite index subgroups of PSL_2(\mathbb Z) using Farey Symbols, (with Chris A. Kurth), Advances in algebra and combinatorics, Proceedings of the second International Congress in Algebra and Combinatorics, World Scientific, (2008) 225-242.
Modular forms for noncongruence subgroups, (with Wen-Ching W. Li and Zifeng Yang), Quarterly Journal of Pure and Applied Mathematics, Volume 1, No. 1, 205-221, 2005.
Recent Grants and Fellowships:
Association for Women in Mathematics Ruth. I. Michler Memorial Prize 2012-2013 winner
NSF grant #DSM-1001332,2010-2013
NSA Young Investigator Research Grant, 2008-2010
ISU ADVANCE program scholar, 2008-2010
Number theory Foundation seminar fund, 2005-2006 and 2006-2007
AWM-NSF mentoring travel grant, summer 2005 and summer 2006
Foreign Travel Grant, Faculty Senate Committee, Iowa State University, summer 2005
Postdoc at the Institute for Advanced Study, 2002-2003
Liftoff Research Fellowship grant, the Clay Mathematical Institute, 2002.
Pritchard Dissertation Fellowship, Pennsylvania State University, 2002.
Conference or Workshop Organization:
Modular forms and Modularity, 2008 AMS National Meeting Special Session (Co-organizer)
Analytic and algebraic number theory, 2011 AMS sectional meeting special session at Iowa City, (Co-organizer)
Research Experience for Undergraduate (REU)
Fall 2011, Supercongruences in Number Theory
Mentors: Jonas Kibelbek and Ling Long
Undergraduate Students: Ben Sheller, Kevin Moss, Hao Yuan
Former graduate student: Chris Kurth (2009)
Postdocs: Tim Huber (2007-2009), Jonas Kibelbek (2011-present)
Number Theory group at Iowa State University
Last update: Jan. 6, 2012