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 papanikolas@tamu.edu

Schedule

Fall 2012
	Teaching:	Math 653: Algebra I, TuTh 12:45-2:00
Spring 2013
	Teaching:	Math 654: Algebra II, TuTh 11:10-12:25
		Math 416: Modern Algebra II, TuTh 12:45-2:00
	Office Hours:	Wed. & Thurs. 3:00-4:00; 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 special values of analytic functions, including L-series, modular forms, and hypergeometric functions, and their connections with periods and logarithms.

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

Click here for a Complete List of Publications

• The Mahler measure of a Calabi-Yau threefold and special L-values (with M. D. Rogers and D. Samart)
  Submitted for publication, 11 pages. [ PDF | arXiv.org ]

• Identities for Anderson generating functions for Drinfeld modules (with A. El-Guindy)
  Submitted for publication, 18 pages. [ PDF | arXiv.org ]

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

• Explicit formulas for Drinfeld modules and their periods (with A. El-Guindy)
  Journal of Number Theory 133 (2013), no. 6, 1864-1886. [ Journal | arXiv.org ]

• Algebraic independence of values of Goss L-functions at s=1 (with B. A. Lutes)
  Journal of Number Theory 133 (2013), no. 3, 1000-1011. [ 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), no. 1, 123-150. [ Journal | arXiv.org ]

• Algebraic relations among periods and logarithms of rank 2 Drinfeld modules (with C.-Y. Chang)
  American Journal of Mathematics 133 (2011), no. 2, 359-391. [ 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), no. 1, 111-129. [ 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), no. 4, 1137-1154. [ 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), no. 8, 1432-1455. [ Journal | arXiv.org ]

• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
  Inventiones Mathematicae 171 (2008), no. 1, 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), no. 1, 19-28. [ Journal | arXiv.org ]

• A formula and a congruence for Ramanujan's tau-function
  Proceedings of the American Mathematical Society 134 (2006), no. 2, 333-341. [ Journal ]

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

• Arizona Winter School
  Univeristy of Arizona, March 9-13, 2013.
• Texas-Oklahoma Representations and Automorphic Forms IV
  Univeristy of North Texas, March 23-24, 2013.
• Seminar on Complex Analysis and Complex Geometry, University of Houston, March 27, 2013.
• Université Jean Monnet, Saint-Etienne, France, May-June 2013
• Séminaire de Théorie des Nombres de Caen, Université de Caen, France, May 17, 2013.
• Université de Versailles-Saint Quentin, France, May 21, 2013.
• NCTS International Workshop on Transcendence and Number Theory,
  National Center for Theoretical Sciences, Hsinchu, Taiwan, June 22-23, 2013.
• Heights, Modularity, Transcendence, Centre International de Rencontres Mathématiques,
  Luminy, France, May 12-16, 2014.