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 Queen’s University

• B.Sc., Major in Mathematics and Minor in Computer Science and Engineering,  Tsinghua University, China, July 1997

Employments:

• Iowa State University, Assistant Professor 2003-present 

• Institute for Advanced Study, General Member of the academic year 2002-2003 

• Clay Mathematical Institute, Liftoff Research Fellow, summer 2002

Research Interests: Number theory, arithmetic geometry, and algebraic geometry

• Finite index subgroups of the modular group and their modular forms

• Modularity of 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 Études Scientifiques in Bures-sur-Yvette (France), July-August, 2005, Partly supported by ISU foreign travel grant.

• Taiwan National Center for Theoretic Sciences, May 2007

• School of Mathematics & System Sciences, ShanDong University, China, June 2007

• Morningside Center of Mathematics at Chinese Academy of Sciences, China, July 2007

• On modular forms for some noncongruence subgroups of PSL₂(Z) II (with Chris A. Kurth), preprint (2008)

• Computations with finite index subgroups of PSL₂(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.

• The finite index subgroups of the modular group and their modular forms, Fields institute Communications, American Mathematical Society, Volume 54, (to appear)

• On modular forms for some noncongruence subgroups of PSL₂(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

• 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

• 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

• 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

• 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.

• 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.