Matthew A. Papanikolas: Curriculum Vitae

Matthew A. Papanikolas

Department of Mathematics
Texas A&M University
College Station, TX 77843-3368
(979) 845-1615 (office)
(979) 845-6028 (fax)

e-mail: map@math.tamu.edu

Citizenship: USA
Place of birth: Tucson, Arizona

Education

Brown University, Providence, Rhode Island.
Ph.D. in Mathematics, 1998.
Sc.M. in Mathematics, 1993.
Dissertation titled "Canonical heights in characteristic p," written under the direction of Joseph H. Silverman.
Amherst College, Amherst, Massachusetts.
A.B. summa cum laude in Mathematics, 1992.

Employment

Texas A&M University, Associate Professor, 2006-present.
Texas A&M University, Assistant Professor, 2003-2006.
Brown University, Tamarkin Assistant Professor, 2000-2003.
Penn State University, Visiting Assistant Professor, 1998-2000.

Research Interests

Number Theory and Arithmetic Geometry
Transcendental Numbers
Elliptic Curves and Abelian Varieties
Drinfeld Modules and t-Modules

Grants Awarded

National Science Foundation, Special Meetings, 2009-12.
"Southwest Center for Arithmetic Geometry." Co-PI with R. Pries, F. Rodriguez-Villegas, D. Savitt, and D. Thakur.
National Science Foundation, Standard Grant, 2006-09.
"Special Functions and Transcendence."
National Science Foundation, Special Meetings, 2006-09.
"Southwest Center for Arithmetic Geometry." Co-PI with F. Rodriguez-Villegas, D. Savitt, W. Stein, and D. Thakur.
National Science Foundation, Standard Grant, 2003-06.
"Transcendental Numbers and Special Analytic Functions."
National Security Agency, Young Investigator Grant, 2003-05.
"Transcendental Numbers and Special Values of Analytic Functions."

Publications and Preprints

[1]		Periods of Drinfeld modules of arbitrary rank and algebraic independence (with C.-Y. Chang) in preparation.
[2]		Geometric Gamma values and zeta values in positive characteristic (with C.-Y. Chang and J. Yu) submitted for publication, 15 pages.
[3]		Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic (with C.-Y. Chang and J. Yu) submitted for publication, 14 pages.
[4]		Algebraic relations among periods and logarithms of rank 2 Drinfeld modules (with C.-Y. Chang) submitted for publication, 25 pages.
[5]		Algebraic independence of arithmetic gamma values and Carlitz zeta values (with C.-Y. Chang, D. Thakur, and J. Yu) submitted for publication, 14 pages.
[6]		Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms Inventiones Mathematicae 171 (2008), 123-174.
[7]		On the torsion of Jacobians of principal modular curves of level 3^n (with C. Rasmussen) Archiv der Mathematik (Basel) 88 (2007), 19-28.
[8]		A formula and a congruence for Ramanujan's tau-function Proceedings of the American Mathematical Society, 134 (2006), 333-341.
[9]		Extensions of abelian varieties defined over a number field (with N. Ramachandran) Journal of Number Theory 112 (2005), 386-400.
[10]		Combinatorics of traces of Hecke operators (with S. Frechette and K. Ono) Proceedings of the National Academy of Sciences, USA, 101 (2004), 17016-17020.
[11]		Gaussian hypergeometric functions and traces of Hecke operators (with S. Frechette and K. Ono) International Mathematics Research Notices, 2004, no. 60, 3233-3262.
[12]		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.
[13]		p-adic properties of values of the modular j-function (with K. Ono) Galois Theory and Modular Forms, 357-366, Dev. Math., 11, Kluwer, 2004.
[14]		Higher Weierstrass points on X_0(p) (with S. Ahlgren) Transactions of the American Mathematical Society 355 (2003), 1521-1535.
[15]		A Weil-Barsotti formula for Drinfeld modules (with N. Ramachandran) Journal of Number Theory 98 (2003), 407-431.
[16]		Universal norms on abelian varieties over global function fields Journal of Number Theory 94 (2002), 326-342.
[17]		Quadratic twists of modular forms and elliptic curves (with K. Ono) Number Theory for the Millennium III (Urbana, IL, 2000), 73-85, A. K. Peters, 2002.
[18]		Linear independence of Gamma values in positive characteristic (with W. D. Brownawell) Journal für die reine und angewandte Mathematik 549 (2002), 91-148.
[19]		Canonical heights on elliptic curves in characteristic p Compositio Mathematica 122 (2000), 299-313.

Graduate Students Supervised

Brad Lutes, Ph.D. student, Texas A&M University
Valentina Vega, Ph.D. 2009, Texas A&M University
"Hypergeometric functions over finite fields and their relations to algebraic curves"
Jenny Fuselier, Ph.D. 2007, Texas A&M University
"Hypergeometric functions over finite fields and relations to modular forms and elliptic curves"

Teaching Experience

Texas A&M University, Assistant Professor, 2003-2006; Associate Professor, 2006-present.
Brown University, Tamarkin Assistant Professor, 2000-2003.
Penn State University, Visiting Assistant Professor, 1998-2000.
Brown University, Graduate Student Teaching Fellow, 1994-1997. Instructor in the following courses.
The National Cathedral School, Washington, DC, High School Mathematics Teacher, 1993-94. Taught Calculus and Geometry.

Selected Invited Talks

Arithmetic Geometry for Function Fields of Positive Characteristic, Centre de Recerca Matemàtica, Barcelona, April 2010.
Modular Forms and Function Field Arithmetic: Conference in Honor of Jing Yu's 60th Birthday, National Taiwan University, May 2009.
Boston College-MIT Number Theory Seminar, April 2009.
Clemson University, April 2009.
Canadian Number Theory Association X Meeting, July 2008.
University of Münster, June 2008.
University of Duisberg-Essen, June 2008.
Rencontres Arithmétiques de Caen XIX, University of Caen, June 2008.
Southern California Number Theory Day, May 2008.
Arizona Winter School 2008, University of Arizona, March 2008.
University of North Texas Colloquium & Algebra Seminar, November 2007.
University of Texas Number Theory Seminar, October 2007.
Miami University, Oxford, OH, September 2007.
National Center for Theoretical Sciences, Hsinchu, Taiwan, May 2007.
Iowa State Colloquium, April 2007.
Ohio State Number Theory Seminar, February 2007.
AMS Special Session of Arithmetic of Function Fields, New Orleans, LA, January 2007.
Palmetto Number Theory Series, University of South Carolina, December 2006.
Tulane University Colloquium, November 2006.
Penn State Number Theory Seminar, October 2006.
Approximation Diophantienne et Nombres Transcendants, CIRM, Marseille, September 2006.
University of Wisconsin Number Theory Seminar, April 2006.
University of Arizona Colloquium and Number Theory Seminar, February 2006.
Workshop on Arithmetic Geometry of Higher Dimensional Varieties, Fields Institute, Toronto, February 2006.
Joint Meeting of the American Mathematical Society and Taiwanese Mathematical Society, special session, Taichung, Taiwan, December 2005.
Rice University Algberaic Geometry Seminar, August 2005.
Journées Arithmétiques XXIV, Marseille, France, Plenary Speaker, July 2005.
Ohio State University Colloquium and Number Theory Seminar, April 2005.
AMS Special Session on Arithmetic Algebraic Geometry, Atlanta, GA, January 2005.
Groupe d'Étude sur les Problèmes Diophantiens, Université de Paris 7, December 2004.
Texas Christian University Colloquium, November 2004.
University of Maryland Number Theory Seminar, October 2004.
Rice University Colloquium, September 2004.
Academia Sinica, Taipei, Taiwan, July 2004.
National Center for Theoretical Sciences, Number Theory Seminar, Hsinchu, Taiwan, July 2004.
Conference in Honour of Dale Brownawell, University of Waterloo, Ontario, Plenary Speaker, June 2004.
Clemson University REU Colloquium, June 2004.
Illinois Number Theory Conference, Plenary Speaker, May 2004.
University of Texas Number Theory Seminar, February 2004.
AMS Special Session on Arithmetic Algebraic Geometry, Phoenix, AZ, January 2004.

Contributed Talks

Journées Arithmétiques XXV, Edinburgh, Scotland, July 2007.
Eighth Meeting of the Canadian Number Theory Association, Toronto, Ontario, June 2004.
Eighteenth Annual Workshop on Automorphic Forms and Related Topics, UC-Santa Barbara, March 2004.
Seventh Meeting of the Canadian Number Theory Association, Montréal, Québec, May 2002.

Meetings Organized

Arizona Winter School 2010: Topic to be announced, University of Arizona, Tucson, AZ, March 13-17, 2010.
Co-organized with R. Pries, F. Rodriguez-Villegas, D. Savitt, D. Thakur.
Banff International Research Station: t-Motives, Hodge Structures, Transcendence and other Motivic Aspects,
Banff, Alberta, September 28-October 2, 2009. Co-organized with G. Boeckle, D. Goss, and U. Hartl.
Arizona Winter School 2009: Quadratic Forms, University of Arizona, Tucson, AZ, March 14-18, 2009.
Co-organized with F. Rodriguez-Villegas, D. Savitt, W. Stein, D. Thakur.
Arizona Winter School 2008: Special Functions and Transcendence, University of Arizona, Tucson, AZ, March 15-19, 2008.
Co-organized with F. Rodriguez-Villegas, D. Savitt, W. Stein, D. Thakur.
Arizona Winter School 2007: p-adic Geometry, University of Arizona, Tucson, AZ, March 10-14, 2007.
Co-organized with F. Rodriguez-Villegas, D. Savitt, W. Stein, D. Thakur.
American Mathematical Society Joint Meetings, San Antonio, TX, January 12-15, 2006.
Special session on Arithmetic Geometry and Modular Forms, co-organized with Ahmad El-Guindy.
ArithmeTexas 2005, Texas A&M University, College Station, TX, April 2-3, 2005.
Co-organized with Paula Cohen.
American Mathematical Society Eastern Section Meeting, Boston, MA, October 1-2, 2002.
Special session on Number Theory and Arithmetic Geometry, co-organized with Siman Wong.

Professional Service

Texas A&M Mathematics executive committee, 2007-09.
Texas A&M Mathematics Awareness Month committee, 2006-09.
Texas A&M Mathematics post-doctoral hiring committee, 2006-07.
Texas A&M Number Theory Seminar, co-organizer, 2003-06.
Mathematical Reviews, reviewer, 2001-05.
Brown Algebra Seminar, co-organizer, 2000-03.
Brown Mathematics Colloquium, co-organizer, 2000-02.
Undergraduate Advisor, Brown University, 2000-01
Referee for Acta Arithmetica, Archiv der Mathematik (Basel), Compositio Mathematica, Journal of Number Theory, Mathematical Research Letters, Mathematics of Computation, Mathematische Nachrichten, Proceedings of the American Mathematical Society, Ramanujan Journal, Transactions of the American Mathematical Society, 1999-2009.

Honors and Awards

National Center for Theoretical Sciences, Hsinchu, Taiwan, July 2004.
Invited visiting researcher.
National Science Foundation Travel Grant, 2002.
To attend the International Congress of Mathematicians in Beijing, China.
Erwin Schrödinger Institute, Vienna, Austria, June 2002.
Invited visiting researcher.
National Science Foundation Travel Grant, 2000.
To attend AMS Mathematical Challenges for the 21st Century in Los Angeles, CA.
Robert H. Breusch Prize in Mathematics, Amherst College, 1992.
For undergraduate thesis work.
Phi Beta Kappa membership, Amherst College, 1992.

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Last modified on May 18, 2009