Matt Papanikolas Professor Department of Mathematics Texas A&M University College Station, TX 77843-3368 Office: Milner 321 Dept: Fax: (979) 845-7554 (979) 845-6028 Email: map@math.tamu.edu

Schedule

Fall 2011
	Teaching:	Math 470: Communications & Cryptography, TuTh 12:45-2:00
Spring 2012
	Teaching:	Math 172.200: Honors Calculus II, TuTh 2:20-3:35
		Math 172.504: Calculus II, TuTh 3:55-5:10
	Office Hours:	Wed. & Thurs. 10:45-11:45; also by appointment

Research Interests

Number theory and arithmetic geometry. I'm interested in elliptic curves and Drinfeld modules, and in particular I work on canonical heights, special values of analytic functions, L-series and modular forms.

Texas A&M Number Theory Group

Texas A&M Number Theory Seminar

Wednesdays, 1:45-2:45, Milner 317

Southwest Center for Arithmetic Geometry

I am currently on the organizing committee for the Arizona Winter School, held annually in March. Please send your students!

Proceedings of the American Mathematical Society

I am an editor in Number Theory for Proceedings of the AMS.

Education

Ph.D. in Mathematics, Brown University, 1998.
A.B. in Mathematics, Amherst College, 1992.

Curriculum Vitae

• My current CV is available here.
• My research is currently sponsored by a grant from the National Science Foundation.

Teaching Information

• Information on courses taught at Texas A&M is available here.

Selected Publications and Preprints (Complete List)

• A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform (with D. McCarthy)
  Submitted for publication, 16 pages. [ PDF | arXiv.org ]

• Explicit formulas for Drinfeld modules and their periods (with A. El-Guindy)
  Submitted for publication, 20 pages. [ PDF | arXiv.org ]

• A rapid introduction to Drinfeld modules, t-modules, and t-motives (with W. D. Brownawell)
  Submitted for publication, 23 pages. [ PDF ]

• Algebraic independence of values of Goss L-functions at s=1 (with B. A. Lutes)
  Journal of Number Theory, in press, 12 pages. [ Journal | arXiv.org ]

• Algebraic independence of periods and logarithms of Drinfeld modules
  (with C.-Y. Chang and with an appendix by B. Conrad)
  Journal of the American Mathematical Society 25 (2012), 123-150. [ Journal | arXiv.org ]

• Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic
  (with C.-Y. Chang and J. Yu)
  Algebra & Number Theory 5 (2011), 111-129. [ Journal | arXiv.org ]

• Algebraic relations among periods and logarithms of rank 2 Drinfeld modules (with C.-Y. Chang)
  American Journal of Mathematics 133 (2011), 359-391. [ Journal | arXiv.org ]

• Geometric Gamma values and zeta values in positive characteristic (with C.-Y. Chang and J. Yu)
  International Mathematics Research Notices 2010 (2010), 1432-1455. [ Journal | arXiv.org ]

• Algebraic independence of arithmetic gamma values and Carlitz zeta values (with C.-Y. Chang, D. Thakur, and J. Yu)
  Advances in Mathematics 223 (2010), 1137-1154. [ Journal | arXiv.org ]

• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
  Inventiones Mathematicae 171 (2008), 123-174. [ Journal | arXiv.org ]

• On the torsion of Jacobians of principal modular curves of level 3^n (with C. Rasmussen)
  Archiv der Mathematik (Basel) 88 (2007), 19-28. [ Journal | arXiv.org ]

• A formula and a congruence for Ramanujan's tau-function
  Proceedings of the American Mathematical Society 134 (2006), 333-341. [ Journal ]

• Extensions of abelian varieties defined over a number field (with N. Ramachandran)
  Journal of Number Theory 112 (2005), 386-400. [ Journal | arXiv.org ]

• Combinatorics of traces of Hecke operators (with S. Frechette and K. Ono)
  Proceedings of the National Academy of Sciences, USA, 101 (2004), 17016-17020. [ Journal ]

• Gaussian hypergeometric functions and traces of Hecke operators (with S. Frechette and K. Ono)
  International Mathematics Research Notices, 2004, no. 60, 3233-3262. [ Journal ]

• Determination of the algebraic relations among special Gamma-values in positive characteristic
  (with G. W. Anderson and W. D. Brownawell)
  Annals of Mathematics 160 (2004), 237-313. [ Journal | arXiv.org ]

Graduate Students

• Detchat Samart, Ph.D. student, Texas A&M University
  
• Brad Lutes, Ph.D. 2010, Texas A&M University
  "Special values of the Goss L-function and special polynomials" [ TAMU Library | PDF ]
• Valentina Vega, Ph.D. 2009, Texas A&M University
  "Hypergeometric functions over finite fields and their relations to algebraic curves" [ TAMU Library ]
• Jenny Fuselier, Ph.D. 2007, Texas A&M University
  "Hypergeometric functions over finite fields and relations to modular forms and elliptic curves" [ TAMU Library ]

Upcoming Schedule

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

• Hypergeometric series and their generalizations in algebra, geometry, number theory and physics,
  Institut Henri Poincaré, Paris, May 29 - June 1, 2012.

• Penn State-Göttingen Number Theory Conference, University of Göttingen, August 13-18, 2012.