Paul M. Jenkins

Associate Professor, BYU Mathematics Department, September 2014-present

Assistant Professor, BYU Mathematics Department, January 2009-August 2014

Hedrick Assistant Professor/NSF Postdoctoral Fellow, UCLA Mathematics Department, July 2006-December 2008

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

P. Jenkins and DJ Thornton, Congruences for coefficients of modular functions, submitted for publication, arXiv:1404.0699v1 [math.NT].

P. Jenkins and K. Pratt, Interlacing of zeros of weakly holomorphic modular forms, Proceedings of the American Mathematical Society, Series B 1 (2014), 63-77, arXiv:1308.1123v1 [math.NT].

N. Green and P. Jenkins, Integral traces of weak Maass forms of genus zero odd prime level, submitted for publication, arXiv:1370.2204v1 [math.NT].

A. Haddock and P. Jenkins, Zeros of weakly holomorphic modular forms of level 4, International Journal of Number Theory 10, no. 2 (2014), 455-470, doi: 10.1142/S1793042113501030, arXiv:1305.3896v1 [math.NT].

S. Garthwaite and P. Jenkins, Zeros of weakly holomorphic modular forms of levels 2 and 3, Mathematical Research Letters 20, no. 4 (2013), 657-674, arXiv:1205.7050v2 [math.NT].

N. Andersen and P. Jenkins, Divisibility properties of coefficients of level p modular functions for genus zero primes, Proceedings of the American Mathematical Society 141 (2013), 41-53, arXiv:1106.1188v1 [math.NT].

D. Doud, P. Jenkins and J. Lopez, Two-divisibility of the coefficients of certain weakly holomorphic modular forms, The Ramanujan Journal 28 (2012), no. 1, 89-111, doi: 10.1007/s11139-011-9331-0, arXiv:1105.0684v2 [math.NT].

P. Jenkins and J. Rouse, Bounds for coefficients of cusp forms and extremal lattices, Bulletin of the London Mathematical Society (2011) 43 (5), 927-938, doi: 10.1112/blms/bdr030, arXiv:1012.5991v2 [math.NT].

D. Doud and P. Jenkins, p-adic properties of coefficients of weakly holomorphic modular forms, International Mathematics Research Notices (2010) 2010: 3184-3206; doi: 10.1093/imrn/rnp240, arXiv:0910.2997v1 [math.NT].

W. Duke and P. Jenkins, Integral traces of singular values of weak Maass forms, Algebra and Number Theory 2 (2008), no. 5, 573-593.

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), no. 3, 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), no. 2, 373-393.

P. Jenkins, p-adic properties for traces of singular moduli, International Journal of Number Theory 1 (2005), no. 1, 103-107.

P. Jenkins, Odd perfect numbers have a prime factor exceeding 10^7, Mathematics of Computation 72 (2003), no. 243, 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 moduli and modular forms (minicourse with W. Duke), Building Bridges: 2nd EU/US Summer School on Automorphic Forms and Related Topics, University of Bristol, July 2-3, 2014

Weakly holomorphic modular forms, Yale University SUMRY colloquium, June 12, 2014

Congruences for coefficients of modular functions, Special Session on Recent Developments in Number Theory, AMS Spring Central Sectional Meeting, Texas Tech University, April 12, 2014

Integrality properties of Zagier lifts of prime level, 27th Automorphic Forms Workshop, University College Dublin, Ireland, March 11, 2013

Zeros of weakly holomorphic modular forms of levels 2 and 3, Ramanujan 125, University of Florida, November 5, 2012

Zeros and coefficients of weakly holomorphic modular forms, Special Session on Harmonic Maass Forms and q-series, AMS Fall Western Sectional Meeting, University of Arizona, October 28, 2012

Zeros and coefficients of weakly holomorphic modular forms, Texas A&M University Number Theory Seminar, October 17, 2012

Zeros of weakly holomorphic modular forms of levels 2 and 3, 1st EU-US Conference on Automorphic Forms and Related Topics, RWTH Aachen University, Germany, August 8, 2012

Zeros of weakly holomorphic modular forms of level 2, 26th Automorphic Forms Workshop, University of British Columbia, April 27, 2012

Bounds for coefficients of cusp forms and extremal lattices, Special Session on Modular Forms, Elliptic Curves, and Related Topics, AMS Fall Southeastern Section Meeting, Wake Forest University, September 24, 2011

Cryptography, Bucknell University Mathematics Department Student Colloquium, April 28, 2011

Weakly holomorphic modular forms, Bucknell University Mathematics Department Distinguished Visiting Professor, April 25, 2011

Bounds for coefficients of cusp forms and extremal lattices, 25th Automorphic Forms Workshop, Oregon State University, March 26, 2011

Bounds for coefficients of cusp forms and extremal lattices, Conference on Modular Forms and Mock Modular Forms and their Applications in Arithmetic, Geometry, and Physics, International Centre for Theoretical Physics, Trieste, Italy, March 18, 2011

Weakly holomorphic modular forms, Wake Forest University, Department of Mathematics Colloquium, October 28, 2010

Coefficient congruences for weakly holomorphic modular forms of integral weight, Special Session on Automorphic Forms and Number Theory, AMS Fall Western Section Meeting, UCLA, October 9, 2010

Congruences for coefficients of weakly holomorphic modular forms, University of Illinois at Urbana-Champaign Number Theory Seminar, April 29, 2010

Congruences for coefficients of weakly holomorphic modular forms, University of Wisconsin-Madison Number Theory Seminar, April 27, 2010

p-adic properties of coefficients of weakly holomorphic modular forms, 24th Automorphic Forms Workshop, University of Hawaii, March 23, 2010

Coefficient congruences for certain weakly holomorphic modular forms, Mock theta functions and applications in combinatorics, algebraic geometry, and mathematical physics, Max Planck Institute for Mathematics, Bonn, Germany, May 26, 2009

What is cryptography?, 2009 CURM Conference and MAA Intermountain Section Meeting, Brigham Young University, March 20, 2009

Coefficients and lifts of modular forms on Gamma_0(3), 23rd Annual Workshop on Automorphic Forms and Related Topics, Bucknell University, March 13, 2009

On singular values of Maass forms, Special Session on Automorphic and Modular Forms in Number Theory, Joint Mathematics Meetings, Washington DC, January 6, 2009

Zeros of weakly holomorphic modular forms, Western Number Theory Conference, Colorado State University, December 16, 2008

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

Cryptography, Bingham High School, May 20, 2014

Weakly holomorphic modular forms, BYU Topics in Advanced Mathematics Seminar, April 11, 2013

Cryptography, BYU High School Mathematics Banquet, November 10, 2011

Bounds for coefficients of cusp forms and extremal lattices, BYU Number Theory Seminar, November 1, 2011

Undergraduate mathematics research at BYU, BYU Seminar in Mathematics (Math 221), October 27, 2011

Cryptography, BYU middle school math camp, June 21, 2011

Cryptography, BYU Seminar in Mathematics (Math 221), September 16, 2010

Cryptography, BYU REU, July 22, 2010

Cryptography, BYU High School Mathematics Banquet, November 5, 2009

p-adic properties of coefficients of weakly holomorphic modular forms, BYU Number Theory Seminar, October 13, 2009

Cryptography, BYU Seminar in Mathematics (Math 221), September 24, 2009

Cryptography, BYU REU, July 16, 2009

Weakly holomorphic modular forms, BYU Mathematics Department Colloquium, December 2, 2008

Integral traces of singular values of weak Maass forms, BYU Number Theory Seminar, October 14, 2008

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 Cryptography

Calculus I

Number Theory

Modular Forms

Algebraic Number Theory

Analytic Number Theory

The Mathematics of Secrecy

Abstract Algebra 1

Abstract Algebra 2

Fundamentals of Mathematics

Combinatorics

Calculus II

Students

Graduate Students

Nathan Green, MS 2013, fall 2011-summer 2013

Chris Hettinger, MS 2014, spring 2012-summer 2014

Undergraduate Research Students

Michael Griffin, fall 2009-winter 2011 (with Darrin Doud)

Nick Andersen, summer 2010-spring 2011 (with Darrin Doud)

Adele Lopez, winter 2010-summer 2012 (with Darrin Doud)

Kyle Pratt, spring 2012-present

Andrew Haddock, spring 2012-present

DJ Thornton, spring 2012-present

Mason Victors, fall 2010-summer 2011

Bradford Tuckfield, fall 2010-summer 2011

Chris Guzman, fall 2010-summer 2011

Benjamin Herrera, spring 2013-present

Chris Hettinger, winter 2011-winter 2012 (with Darrin Doud)

Nathan Green, spring 2011-fall 2011

Jocelyn Peck, winter 2010-winter 2011 (with Darrin Doud)

Joseph Keller, summer 2009-summer 2010

Leo Teemant, summer 2009-summer 2010

Tim Krumwiede, summer 2009-summer 2010

Kevin Childers, winter 2010 (with Darrin Doud)

Jooyoun Lee, fall 2009 (with Darrin Doud)

Awards

PI, NSF grant DMS-1404066, Automorphic Forms Workshop 2014 (with David Cardon and Darrin Doud), Spring 2014, Moab, UT

Distinguished Citizenship Award, Brigham Young University Department of Mathematics, 2013

PI, NSA grant 121015, Automorphic Forms Workshop 2014 (with David Cardon and Darrin Doud), Spring 2014, Moab, UT

Collaboration Grant for Mathematicians (#281876), Simons Foundation, 2013-2018

Co-PI, BYU ORCA Mentoring Environment Grant (with David Cardon, Darrin Doud, and Pace Nielsen), BYU Computational Number Theory Research Group, 2013-2014

Distinguished Mentoring Award, Brigham Young University Department of Mathematics, 2011

PI, BYU ORCA Mentoring Environment Grant (with David Cardon, Darrin Doud, and Pace Nielsen), BYU Computational Number Theory Research Group, 2011-2012

Project NExT Fellow, 2009-2010

Co-PI, NSF grant DMS-0910714, Graduate workshop on zeta functions, L-functions and their applications, Summer 2009, Orem, UT

Robert Sorgenfrey Distinguished Teaching Award, UCLA Mathematics Department, 2008

National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship, DMS-0603271, 2006-2010

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:

Conferences Attended

(Titles of talks not previously referenced are noted.)

Building Bridges: 2nd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, University of Bristol, July 2-9, 2014

28th Automorphic Forms Workshop, Moab, Utah, May 12-16, 2014

Applications of Automorphic Forms in Number Theory and Combinatorics, Louisiana State University, April 13-15, 2014

AMS Spring Central Sectional meeting, Texas Tech University, April 12, 2014

Joint Mathematics Meetings, Baltimore, January 15-17, 2014

Automorphic Forms and L-functions, TU Darmstadt, Germany, March 17-19, 2013

27th Automorphic Forms Workshop, University College Dublin, March 11-14, 2013

Ramanujan 125, University of Florida, November 5-7, 2012

AMS Fall Western Sectional meeting, University of Arizona, October 27-28, 2012

1st EU-US Conference on Automorphic Forms and Related Topics, RWTH Aachen University, Germany, July 30-August 10, 2012

26th Automorphic Forms Workshop, University of British Columbia, April 26-29, 2012

Joint Mathematics Meetings, Boston, January 4-6, 2012

AMS Fall Southeastern Section Meeting, Wake Forest University, September 24-25, 2011

25th Automorphic Forms Workshop, Oregon State University, March 23-26, 2011

Conference on Modular Forms and Mock Modular Forms and their Applications in Arithmetic, Geometry, and Physics, International Centre for Theoretical Physics, Trieste, Italy, March 14-18, 2011

The Number Theory of Partitions, Emory University, January 21-23, 2011

Western Number Theory Conference, Utah Valley University, December 15-18, 2010

AMS Fall Western Section Meeting, UCLA, October 9-10, 2010

MAA Mathfest, Pittsburgh, Pennsylvania, August 4-7, 2010

Prospects in q-series and modular forms, University College Dublin, Ireland, July 14-16, 2010

24th Automorphic Forms Workshop, University of Hawaii, March 22-26, 2010

Mock modular forms in combinatorics and arithmetic geometry, AIM, Palo Alto, March 8-12, 2010

Joint Mathematics Meetings, San Francisco, January 13-16, 2010

MAA Mathfest, Portland, Oregon, August 5-8, 2009

2009 Graduate Workshop on Zeta Functions, L-Functions and their Applications, Utah Valley University, June 1-4, 2009

Mock theta functions and applications in combinatorics, algebraic geometry, and mathematical physics, Max Planck Institute for Mathematics, Bonn, Germany, May 25-29, 2009

2009 CURM Conference and MAA Intermountain Section Meeting, Brigham Young University, March 20, 2009

23rd Annual Workshop on Automorphic Forms and Related Topics, Bucknell University, March 10-13, 2009

Joint Mathematics Meetings, Washington DC, January 5-8, 2009

Western Number Theory Conference, Colorado State University, December 15-18, 2008

Combinatory Analysis 2008: Partitions, q-series, and Applications, Penn State University, December 5-7, 2008

Southern California Number Theory Day, University of California, Irvine, October 25, 2008

Canadian Number Theory Association X, University of Waterloo, July 13-18, 2008

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

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