Paul M. Jenkins

Hedrick Assistant Professor/NSF Postdoctoral Fellow, UCLA Mathematics Department, 2006-present

Education

Ph.D. Mathematics, May 2006, University of Wisconsin-Madison.  Advisor:  Ken Ono

M.S. Mathematics, August 2002, Brigham Young University.  Advisor:  David Clark

B.S. Mathematics with University Honors and Summa Cum Laude, December 2000, Brigham Young University.

Publications

W. Duke and P. Jenkins, Integral traces of singular values of weak Maass forms, Algebra and Number Theory, to appear.

W. Duke and P. Jenkins, On the zeros and coefficients of certain weakly holomorphic modular forms, Pure and Applied Mathematics Quarterly 4 (2008), no. 4, 1327-1340.

P. Jenkins and K. Ono, Divisibility criteria for class numbers of imaginary quadratic fields, Acta Arithmetica 125 (2006), 285-289.

P. Jenkins, Traces of singular moduli, modular forms, and Maass forms, Dissertation (Ph.D.), University of Wisconsin-Madison, 2006

P. Jenkins, Kloosterman sums and traces of singular moduli, Journal of Number Theory 117 (2006), no. 2, 301-314.

J. Bruinier, P. Jenkins and K. Ono, Hilbert class polynomials and traces of singular moduli, Mathematische Annalen 334 (2006), 373-393.

P. Jenkins, p-adic properties for traces of singular moduli, International Journal of Number Theory 1 (2005), 103-107.

P. Jenkins, Odd perfect numbers have a prime factor exceeding 10^7, Mathematics of Computation 72 (2003), 1549-1554.

P. Jenkins, Isolated inhomogeneous minima of binary quadratic forms, Thesis (M.S.), Brigham Young University, 2002.

P. Jenkins, Odd perfect numbers have a prime factor exceeding 10^7, Honors Thesis, Brigham Young University, 2000.

Selected Presentations

Singular values of weak Maass forms, Hawaii workshop on the arithmetic of modular forms, University of Hawaii, May 21, 2008

Integral traces of singular values of Maass forms, 22nd Annual Workshop on Automorphic Forms and Related Topics, Texas A&M University, March 10, 2008

Integral traces of singular values of Maass forms, University of Wisconsin-Madison Number Theory Seminar, February 14, 2008

Integral traces of singular values of Maass forms, University of Illinois at Urbana-Champaign Number Theory Seminar, February 12, 2008

Traces of singular values of Maass forms, Special Session on Modular Forms and Modularity, Joint Mathematics Meetings, San Diego, California, January 7, 2008

Coefficients and zeros of certain weakly holomorphic modular forms, Illinois Number Theory Fest, University of Illinois at Urbana-Champaign, May 19, 2007

Properties of certain weakly holomorphic modular forms, Special Session on Number Theory in the Southwest, AMS Spring Western Section Meeting, University of Arizona, April 21, 2007

Coefficients and zeros of weakly holomorphic modular forms, Claremont Mathematics Colloquium, Claremont Colleges, April 11, 2007

Zeros of certain weakly holomorphic modular forms, 21st Annual Workshop on Automorphic Forms and Related Topics, University of California at Santa Barbara, March 27, 2007

Zeros of weakly holomorphic modular forms, Special Session on Analytic Number Theory and Modular Forms, AMS Fall Southeastern Section Meeting, University of Arkansas, November 4, 2006

Borcherds products, Zagier duality, and traces of singular moduli, Brigham Young University Mathematics Department Colloquium, February 9, 2006

Maass-Poincare'  series and p-divisibility of traces of singular moduli, Special Session on Arithmetic Geometry and Modular Forms, Joint Mathematics Meetings, San Antonio, Texas, January 13, 2006

p-adic properties of traces of singular moduli, Intersection of Arithmetic Cycles and Automorphic Forms, CRM, Montreal, December 14, 2005

Maass-Poincare'  series and p-divisibility of traces of singular moduli, Texas A&M University Number Theory Seminar, November 30, 2005

Borcherds products and p-adic properties of singular moduli, Brigham Young University Mathematics Department, July 28, 2005

Borcherds products and p-adic properties of singular moduli, ArithmeTexas, Texas A&M University, April 2, 2005

Recent work on traces of singular moduli, 19th Annual Workshop on Automorphic Forms and Related Topics, University of North Texas, March 17, 2005

Kloosterman sums and traces of singular moduli, Additive Number Theory Conference, University of Florida, November 20, 2004

Zagier's generating functions for traces of singular moduli, Arakelov Theory and Modular Forms, NSF FRG Conference, University of Wisconsin-Madison, September 19, 2004

Asymptotics of traces of singular moduli, Canadian Number Theory Association VIII, University of Toronto, June 22, 2004

Asymptotics of traces of singular moduli, Illinois Number Theory Conference, University of Illinois at Urbana-Champaign, May 21, 2004

Asymptotics of traces of singular moduli, 18th Annual Workshop on Automorphic Forms and Related Topics, University of California at Santa Barbara, March 23, 2004

Local Seminar Talks

Integral traces of singular values of Maass forms, UCLA Number Theory Seminar, March 31, 2008

Borcherds products, Zagier duality, and traces of singular moduli, UCLA Number Theory Seminar, January 22, 2007

Borcherds products and p-adic properties of singular moduli, University of Wisconsin-Madison Number Theory Seminar, March 10, 2005

Kloosterman sums and traces of singular moduli, University of Wisconsin-Madison Number Theory Seminar, November 4, 2004

Traces of singular moduli, University of Wisconsin-Madison Number Theory Seminar, December 4, 2003

Odd perfect numbers have a prime factor exceeding 10^7, University of Wisconsin-Madison Number Theory Seminar, September 19, 2002

Odd perfect numbers have a prime factor exceeding 10^7, Brigham Young University Number Theory Seminar, March 20, 2002

Odd perfect numbers have a prime factor exceeding 10^7, Brigham Young University Graduate Student Seminar, October 25, 2001

Teaching

Mathematical Cryptology

Combinatorics

Calculus II

Instructor, Calculus I

Prepared syllabus and lectures, wrote and graded exams and quizzes, assigned homework

Coordinator, Calculus I

Assisted in mentoring new TAs, including observing classes, providing feedback on teaching ideas and techniques, and assisting with formal TA training before and during the semester; taught two discussion sections

Teaching Assistant, Discrete Mathematics

Taught four discussion sections, graded homework and exams

Teaching Assistant, College Algebra (computer-based)

Provided assistance to students working on assignments in computer lab

Teaching Assistant, Calculus I

Taught two or three discussion sections, including writing quizzes and grading homework and exams

Awards

Robert Sorgenfrey Distinguished Teaching Award, UCLA Mathematics Department, 2008

National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship, 2006-2009

Excellence in Mathematical Research Award, May 2006, University of Wisconsin-Madison (two awards given in department)

VIGRE Graduate Fellowship, University of Wisconsin-Madison, 2002-2003, 2004-2005

Graduate Research Award, April 2001, Brigham Young University Department of Mathematics (two awards given in department)

National Science Foundation Graduate Research Fellowship, Honorable Mention, 2001

National Merit Scholarship, 1995-2000

Professional Service

Reviewer for Mathematical Reviews

Referee work, Proceedings of the American Mathematical Society

Conferences Attended

(Titles of talks not previously referenced are noted.)

Hawaii workshop on the arithmetic of modular forms, University of Hawaii, May 21-24, 2008

Recent Developments in Number Theory:  Selmer Groups, L-functions, and Galois Deformations, UCLA, March 24-29, 2008

22nd Annual Workshop on Automorphic Forms and Related Topics, Texas A&M University, March 10, 2008

Joint Mathematics Meetings, San Diego, California, January 7-8, 2008

Illinois Number Theory Fest, University of Illinois at Urbana-Champaign, May 16-20, 2007

Fields Medalists Symposium, UCLA, April 26, 2007

21st Annual Workshop on Automorphic Forms and Related Topics, University of California at Santa Barbara, March 24-27, 2007

SAGE Days 3, IPAM, Los Angeles, February 17-21, 2007

AMS Fall Southeastern Section Meeting, University of Arkansas, November 3-4, 2006

Southern California Number Theory Day, University of California, Irvine, October 14, 2006

Harvey Mudd College Mathematics Conference on Enumerative Combinatorics, October 6-7, 2006

Joint Mathematics Meetings, San Antonio, Texas, January 12-15, 2006

Intersection of Arithmetic Cycles and Automorphic Forms, CRM, Montreal, December 12-16, 2005

Borcherds products and p-adic properties of singular moduli, Midwest Number Theory Conference for Graduate Students III, University of Wisconsin-Madison, November 5-6, 2005

Midwest Number Theory Day, University of Wisconsin-Madison, November 4, 2005

Singular Moduli and Equidistribution, NSF FRG Conference, University of Maryland, October 7-9, 2005

Bretton Woods Workshop on Multiple Dirichlet Series, Bretton Woods, New Hampshire, July 11-14, 2005

Gauss-Dirichlet Conference, Göttingen, Germany, June 20-24, 2005

ArithmeTexas, Texas A&M University, April 2-3, 2005

19th Annual Workshop on Automorphic Forms and Related Topics, University of North Texas, March 17-20, 2005

Kloosterman sums and traces of singular moduli, Midwest Number Theory Conference for Graduate Students and Recent PhDs II, University of Illinois at Urbana-Champaign, February 5-6, 2005

Additive Number Theory Conference, University of Florida, November 17-20, 2004

Arakelov Theory and Modular Forms, NSF FRG Conference, University of Wisconsin-Madison, September 16-19, 2004

Canadian Number Theory Association VIII, University of Toronto, June 2004

Illinois Number Theory Conference, University of Illinois at Urbana-Champaign, May 2004

18th Annual Workshop on Automorphic Forms and Related Topics, University of California at Santa Barbara, March 2004

Traces of singular moduli, Midwest Number Theory Conference for Graduate Students and Recent PhDs, University of Wisconsin-Madison, October 2003

Isolated inhomogeneous minima of binary quadratic forms, Brigham Young University Spring Research Conference, March 16, 2002

Wasatch Topology Conference, Park City, UT, December 2001

MSRI Summer Graduate Program on Minimal Surfaces, Berkeley, CA, June-July 2001