Ling Long

Curriculum Vitae

Contact Information:

Department of Mathematics / Phone: 515-294-8150
IowaStateUniversity / Email:
Ames, Iowa50011, USA. / URL:

Current Research Interests:

  • Number Theory and its applications

Education:

  • PennsylvaniaStateUniversity, University Park, PA

Ph.D. in Mathematics, 2002

Thesis: Modularity of elliptic surfaces

Thesis Advisor: Wen-Ching Winnie Li at PennsylvaniaStateUniversity

Joint Thesis Advisor: Noriko Yui at Queen’s University

  • TshinghuaUniversity, BeijingChina

B.Sc., Major in Mathematics and Minor in Computer Science and Engineering

Employment History:

2003–present / Assistant Professor, IowaStateUniversity
2002–2003 / General Member , Institute for Advanced Study (Princeton, NJ).
Summer 2002 / Liftoff Research Fellow, Clay Mathematical Institute

Research Grants:

  • NSA Young Investigators Grant:

– Noncongruence modular form, PI, $30,000.00, 2008-2010.

  • AIM-NSF Grant Award:

–Noncongruence modular form and modularity, AIM workshop in August 2009, Principal Organizer, $40,000 (estimated).

  • Number Theory Foundation Grants:

– Number Theory Seminar at ISU,PI, $2,000, 2005-2007

  • AWM-NSF Award:

– Mentoring Travel Grant, $4,000, 2005-2006

  • ISU Faculty Senate Foreign Travel Grant, summer 2006
  • NSF Grant No. DMS 97-29992, 2002-2003
  • Clay Mathematical Institute

– Liftoff Research Fellowship Grant, $4,000, 2002.

Professional Memberships:

  • American Mathematical Society (AMS)
  • AssociationofWomeninMathematics (AWM)

Publications:

Published/Accepted Papers:

[1]OnAtkinand Swinnerton-Dyercongruencerelations(3),JournalofNumberTheory,doi:10.1016/j.jnt.2008.02.014, in press, (17pp).

[2]§ComputationswithfiniteindexsubgroupsofPSL2(Z)usingFareySymbols,(withChris,Kurth),accepted,toappearonICACconferenceproceedings(16pp).

[3]Onmodularformsforsomenoncongruencesubgroupsofthemodulargroup,(withChris,Kurth),DOI:10.1016/j.jnt.2007.10.007,JournalofNumberTheory, in press, (21pp).

[4]§Finiteindexsubgroupsofthemodulargroupandtheirmodularforms,ModularFormsandStringDuality,theFieldsInstituteCommunications,Volume54,toappear,(20pp)

[5]†OnAtkinandSwinnerton-Dyercongruencerelations(2)(withA.O.L.AtkinandWenchingWinnieLi),MathematischeAnnalen,Volume340,No.2(2008)335-358.

[6]†ReciprocityforStirlingandmulti-restrictednumbers(withJiYoungChoi,Siu-HungNgandJonathanSmith),JournalofCombinatoricsTheory,seriesA,Volume113 (2006)1050-1060.

[7]AshortproofofMilne’sformulaeforsumsofintegersquares,(withYifanYang),theInternationalJournalofNumberTheory,Vol1no.4(2005)533-551.

[8]OnAtkinandSwinnerton-Dyercongruencerelations,(withWen-ChingW.LiandZifengYang)JournalofNumberTheoryVolume113,No.1(2005)117-148.

[9]Modularformsfornoncongruencesubgroups,(withWen-ChingW.LiandZifengYang),Quarterly JournalofPureandAppliedMathematics,Volume1,No.1,205-221,2005.

[10]OnShioda-InosestructuresofoneparameterfamiliesofK3surfaces,JournalofNum-berTheory,2004,Volume109,No.2(2004)299-318.

International Collaborations

§ Original research articles in book series/refereed major conference proceedings

† Inter-institutional Collaborations

‡ Expository articles in book series/refereed major conference proceedings

[11]L-seriesofcertainellipticsurfaces,CanadianMathematicalBulletin,Volume46,No.4(2003),546-558.

[12]‡OnaShioda-InosestructureofafamilyofK3surfaces,Calabi-YauVarietiesandMir-rorSymmetry,FieldsInstituteCommunications38,AmericanMathematicaSociety,ProvidenceRI(2003)201-207.

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Selected Financial Support for Conferences or Scholarly Visitations:

  1. Travel and local expenses (2 days) covered by number theory seminar fund of University of Illinois at Urbana-Champaign, March, 2008
  2. Travel and local expenses (5 days) covered by AIM for attending ``Computing arithmetic spectra" workshop, American Institute of Mathematics, March, 2008.
  3. Travel and local expenses (3 days) covered by Midwest Number Theory Days conference, University of Illinois at Chicago, March 2008.
  4. Travel and local expenses (3 weeks) covered by MorningSide Institute, Beijing, China, July, 2007.
  5. Local expenses (1 day) covered by CapitalNormalUniversity, Beijing, China, July 20, 2007.
  6. Travel and local expenses (14 days) covered by the Center of Mathematical Sciences at Zhejiang University, China, June 10-24, 2007.
  7. Travel and local expenses (7 days) covered by Shandong University, China, June 3-10, 2007.
  8. Travel and local expenses (2 days) covered by the University of Hong Kong, May 31-June 1, 2007.
  9. Travel expenses and local expenses (18 days) covered by the NationalCenter for Theoretical Sciences, Tainan, Taiwan, May, 2007.
  10. Travel and local expenses (3 days) covered by the Clemson University, April 2007.
  11. Registration fee covered by the host to attend the Canadian Mathematical Society Winter Meeting, December, 2006.
  12. Local expenses (5 days) covered by Banff BIRSconference center for attending ``Modular Forms and String Duality" workshop, June, 2006.
  13. Faculty Senate Foreign Travel Grant, summer 2005
  14. $4000 NSF-AWM mentoring travel grant, summer 2005 and 2006.
  15. Travel and local expenses (2 days) covered by the number theory seminar fund of University of Illinois at Urbana-Champaign, April 2005.
  16. Travel and honorarium covered by the mathematics colloquium fund of University of Iowa, March, 2005.
  17. $500 NSF travel grant for attendingCanadianNumber Theory Conference VIII,University of Toronto, Canada, June, 2004.
  18. Travel and local expenses (2 days) covered by the number theory conference fund of University of Illinois at Urbana-Champaign, May 2004.
  19. Travel, local expenses and honorarium (3 days) covered by the number theory seminar fund of Louisiana State University, April 2004.
  20. Travel, local expenses and honorarium (2 days) covered by the number theory seminar fund of University of Wisconsin-Madison, April 2004.
  21. Travel and lodging (4 days) covered by Arizona University for attending Arizona Winter School, March 2004
  22. Travel and local expenses (2 days) covered by the number theory seminar fund of Johns Hopkins University, February 2004.

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Presentations since Fall 2003:

Invited Conference Talks:

  1. On Atkin and Swinnerton-Dyer congruences, AMS sectional meeting, Louisiana State University, March 29.
  2. **On Atkin and Swinnerton-Dyer congruences}, Midwest Number Theory Days, March 7-8, UIC.
  3. Modular forms for certain noncongruence subgroups, San Diego AMS general meeting, January 2008.
  4. Modularity of algebraic varieties, Fields institute workshop on arithmetic and geometry of algebraic varieties with special emphasis on Calabi--Yau varieties and mirror symmetry, Nov. 2007.
  5. Noncongruence subgroups of the modular group, International congress on algebra and combinatorics (ICAC),Beijing, China, July 9, 2007.
  6. **Modularity of noncongruence cuspforms, National Center for Theoretical Sciences (NCTS) conference on Galois Representation and Function Field Arithmetic, Taiwan, May 17, 2007.
  7. **On the Coefficients of Noncongruence Modular Forms, Canadian Mathematical Society Winter Meeting, Dec. 11, 2006.
  8. **Modular Forms for Noncongruence Subgroups, Banff BIRS conference on Modular Forms and String Duality. Banff, Alberta,Canada, June 5, 2006.
  9. The modularity of certain elliptic modular surfaces, Weekend workshop on Arithmetic and Geometry of Algebraic Varieties with Special Emphasis on Calabi-Yau Varieties and Mirror Symmetry, Fields Institute, Toronto, Canada, March 2006.
  10. Atkin and Swinnerton-Dyer congruence and the modularity for certain noncongruence cuspforms, AMS general meeting, San Antonio, January 15, 2006.
  11. The Picard-Fuchs equations of certain one-parameter families of K3 surfaces, Workshop on Arithmetic and Geometry of Algebraic Varieties, Fields Institute, Canada, March 6, 2005.
  12. **On cuspforms of non-congruence subgroups, Illinois number theory conference, University of Illinois at Urbana-Champaign, May 21 2004.
  13. On cuspforms of non-congruence subgroups, Workshop on Arithmetic and Geometry of Algebraic Varieties, Fields Institute, Canada, November 2003.

Invited Collouium/Seminar Talks:

  1. **Finite index subgroups of the modular group and their modular forms, Number Theory Seminar, UIUC, March 27.
  2. **Modular forms for congruence subgroups, BeijingCapitalNormalUniversity, Invited talk, Beijing, China, July, 2007.
  3. **Modular forms for noncongruence subgroups, MorningSide institute, China, July 9, 2007.
  4. **Finite index subgroups of the modular group and their modular forms, Zhejiang University, China, June 16, 2007
  5. **Finite index subgroups of the modular group and their modular forms,Shan Dong University, China, June 6, 2007.
  6. **Finite index subgroups of the modular group and their modular forms,Hong KongUniversity, June 1, 2007.
  7. **Modular forms for some noncongruence subgroups, NationalCenter for Theoretical Sciences (NCTS), Taiwan, May 22, 2007.
  8. **Finite index subgroups of the modular group and their modular forms,ClemsonUniversity, April 13, 2007.
  9. **Eisenstein series and representing natural numbers as sum of integer squares, number theory seminar, University of Illinois at Urbana-Champaign, April 2005.
  10. **Modular forms for noncongruence subgroup of $SL_2(Z)$, colloquium talk, University of Iowa, March 30, 2005.
  11. **On Atkin-Swinnerton-Dyer congruence relations, algebra and number theory seminar, LouisianaStateUniversity, April 19, 2004.
  12. **On cuspforms of non-congruence subgroups, number theory seminar, University of Wisconsin-Madison, April 15 2004.
  13. **On Atkin-Swinnerton-Dyer congruence relations, number theory seminar, JohnsHopkinsUniversity, February 2004.

Contributed Talks:

  1. A short proof of Milne's formulae for sums of integer squares, ArithmeTexas, University of Texas at A\&M, April 3rd2005.
  2. **On Atkin-Swinnerton-Dyer congruence relations, Canadian Number Theory Conference VIII, University of Toronto, Canada, June 20, 2004.

Departmental Seminar Talks:

  1. Zeros of Eisenstein series, Hypergeometric seminar, March 5 and April 16, 2008.
  2. Triangular groups and Hypergeometric series, Hypergeometric seminar, Oct. 2007.
  3. Hypergeometric series and Mahler measure, Hypergeometric seminar, Sep. 2007.
  4. Fermat curves and modular curve, algebra/combinatroics/number theory seminar, IowaStateUniversity, Sep. 2007.
  5. Continued fractions and their applications, ISU Math Club seminar, January 2007.
  6. Finite index subgroups of PSL(2,Z) and their modular functions, Combinatorics/Algebra/Number Theory seminar. Nov. 2006.
  7. $q$-hypergeometric functions and $q$-identities, Algebra/number theory seminar, IowaStateUniversity, February 6, 2006.
  8. Modern approaches to counting problems, IowaStateUniversity undergraduate math club talk, Oct. 30, 2005.
  9. Multi-restricted Stirling numbers, Combinatorics/Algebra/Number Theory seminar, Oct. 24, 2005.
  10. Modern approaches to counting problems-partition and sum of integer squares, IowaCollegiate Mathematics Competition special lecture, IowaStateUniversity, April 2005.
  11. Introduction to elliptic curves, Graduate colloquium, February, 10, 2005.
  12. From congruence to noncongruence modular forms, algebra and combinatorics seminar, November 29, 2004.
  13. Representing natural numbers as sums of integer squares, algebra and combinatorics seminar, IowaStateUniversity, March, 2004.
  14. Elliptic surface, $A-D-E$ Dynkin diagrams and their applications, algebra and combinatorics seminar, December 2003.
  15. Modular forms of congruence and non-congruence subgroups, Colloquium talk, August 2003.

Other Participated Conferences:

  1. **AIM workshop on ``Computing arithmetic spectra", March 9-14, 2008.
  2. Modularity of GL2 and Beyond, Mathematical Science Research Institute, Nov. 2006.
  3. **Arizona Winter School 2004, University of Texas at Austin, March 2004.

Visitors Hosted:

  1. Winnie Li (PennsylaniaStateUniversity), Dec. 2003.
  2. HelenaVerrill (LouisianaStateUniversity), April 2004.
  3. Ken Ono (University of Wisconsin, Madison), Nov. 2004.
  4. Karl Mahlburg (University of Wisconsin-Madison, April 2005.
  5. Charles Doran (University of Washington, Seattle), April 2005.
  6. Stephanie Treneer (UIUC), April 2005.
  7. Yangbo Ye (University of Iowa, Sep. 2005.
  8. Jerome W. Hoffman (LouisianaStateUniversity), Oct. 2005.
  9. Raghuram, (U of Iowa), Nov. 2005.
  10. Ye Tian, (McGillUniversity), Mar. 2006.
  11. Bruce Berndt (UIUC), Mar. 2006.
  12. Jayce Getz (University of Wisconsin), April 2006.
  13. Kathrin Bringmann (University of Wisconsin), April 2006.
  14. Muthu Krishnamurthy (University of Iowa), Oct. 10, 2006.
  15. Tong Liu (University of Pennsylvania), Feb 2007.
  16. Bin Zhang, (SichuanUniversity), March 2007.
  17. Tim Huber (UIUC) March 2007.
  18. Neal Koblitz(University of Washington), March 2007.
  19. Matt Pananikolas (Texas A&M), April 2007.
  20. Mehmet Haluk Sengun (University of Wisconsin-Madison), Jan.2008.
  21. Ae Ja Yee, (Penn.StateUniversity), April 2008.
  22. George Andrews, (Penn.StateUniversity), April 2008.

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Scholarly Visitations:

  • MorningSide center, Beijing, China, July 2007 (local expenses covered by the host).
  • Center of Mathematical Sciences at Zhejiang University, China, June 10-24, 2007 (travel and local expenses covered by the host).
  • Shandong University, China, June 3-10, 2007 (stipend, travel, and lodging covered by the host).
  • NationalCenterfor Theoretical Sciences, Taiwan, May 12-30, 2007 (stipend, travel, and lodging covered by the host).
  • Penn.StateUniversity, May 16–June 15, 2006. (travel and local expenses covered by an NSF-AWM Travel Grant in part).
  • Institut des Hautes Etudes Scientifiques(IHES), Paris, France, July 22–August 19, 2005. (lodging and local expenses covered by IHES).
  • Penn.StateUniversity, May 16–June 15, 2005.(travel and local expenses covered by an NSF-AWM Travel Grant).

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Conferences Organizer:

  • Modular Forms and Modularity,

AMS General Meeting at San Diego, January 2008, Co-organizer.

  • Noncongruence modular forms and modularity,

American Mathematics Institute (AIM) workshop, August 2009, Principal Organizer.

Referee for Journals/Agencies:

Journal or Agency \Year / 08 / 07 / 04
Proceedings of American Mathematical Society / 1
International Journal of Number Theory / 1
Applied Mathematics and Computing / 1
The Southeast Asian Bulletin of Mathematics / 1
Journal of Combinatorial Theory - Series A / 1
IFIP SEC 2008 Conference proceedings / 2

University Committees:

  • Faculty senator (Spring 2007-present).
  • Faculty mentor for Dinhvan Ha, the McNair Scholars Program (2005-2007).

College Services:

  • Organizer of the following joint events

LAS Miller lecture / George Andrews, Penn.StateUniversity, president elect of American Mathematical Society / April 2008
LAS Miller lecture / Neal Koblitz,University of Washington / March 2007
Mathematics/Computer Science colloquium / Bruce C. Berndt, University of Illinois atUrbana-Champaign / March 2006
Mathematics/Physics Colloquium / Charles Doran,Universityof Washington / March 2005
LAS Miller lecture / Ken Ono, University of Wisconsin / November 2004
  • 3 Computer Science Master Degree Program of Study Committees.

Departmental Committees:

  • Colloquium co-chair (Fall 2004-present).
  • Student Advisor, Pi Mu Epsilon Undergraduate Math Club (Fall 2007).
  • Algebra Qualifier Committee (Fall 2008-present).
  • Program of Study committees (2003-present):

Master / Program / Ph.D. / Program
Chair / 1 / Mathematics
Co-Chair / 1 / Mathematics
Member / 1 / Mathematics / 4 / Mathematics

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Graduate Advising:

Major/co-major Professor of the Ph.D. Students:

  1. Chris Kurth, Mathematics, in progress.
  2. Joohyung Kim, Mathematics, (Ph.D. 2005).

Program of Study Committee member of the following students:

Ph.D. Students:

  1. Ruben Aydinyan, Mathematics, (Ph.D. 2004).
  2. Key One Chung, Mathematics, (Ph.D. 2007).
  3. James, R. Fiedler, Mathematics, (Ph.D. 2007).
  4. Gargi Bhattacharyya, Mathematics, (Current).

Master Students:

  1. Fanghui Qing, computer science, (Master 2005),
  2. Dean Lin,, computer science, in progress
  3. Bachar Chama, , computer science,in progress.

Programs Attended to Advance Teaching:

  • Large Class Faculty Learning Community, Fall 2007- Spring 2008, $1,500 stipend awarded, sponsored by Centerfor Excellence in Learning and Teaching, IowaStateUniversity.
  • Teaching partner program, Spring 2005, sponsored by Centerfor Excellence in Learning and Teaching, IowaStateUniversity.Senior partner, Steve E. Jungst Natural Resource Ecology andManagement Department.

Curriculum Development Activities:

  • Developed an undergraduate number theory course (350)cross-listed to computer science department.

Courses Taught since 2003:

Graduate Courses:

S 2008 / Abstract algebra II 505, IowaStateUniversity
F 2007 / Abstract Algebra I 504, IowaStateUniversity
S 2006 / Topics in Algebra and Number Theory 690G,IowaStateUniversity
S 2005 / Number Theory and Its Applications 690Z,IowaStateUniversity
F 2004 / Galois Theory and Commutative Algebra 690Z,IowaStateUniversity

Undergraduate Courses:

F 2008 / Introduction to proofs 201, IowaStateUniversity
F 2007 / Calculus I 165, IowaStateUniversity
S 2007 / Number Theory 350, IowaStateUniversity
F 2006 / Abstract Algebra I 301,IowaStateUniversity
S 2006 / Number Theory 350, IowaStateUniversity
F 2005 / Introduction to Mathematical Ideas 105, IowaStateUniversity
F 2005 / Abstract Algebra I 301,IowaStateUniversity
F 2004 / Abstract Algebra I 301,IowaStateUniversity
F 2004 / Linear Algebra 317, IowaStateUniversity
F 2003 / Calculus I 165, IowaStateUniversity

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