Curriculum Vitae for Matthew Baker

Office Address:  Home Address:
Deparment of Mathematics  1613 6th St. Apt. E
University of California at Berkeley  Berkeley, CA 94710
Berkeley, CA 94720-3840  (510) 525-2077

baker@math.berkeley.edu

Personal Information:

Date of Birth: January 30, 1973
Birthplace:  Silver Spring, MD
Citizenship: USA

Education:

Ph.D: May 1999, University of California at Berkeley (expected)
BS:  May 1994, University of Maryland at College Park (Summa Cum Laude)

Research Interests:

Arithmetic Algebraic Geometry Number Theory Modular Curves and Modular Forms

Dissertation:

Torsion Points on Modular Curves, (in preparation).

We develop techniques to study a general conjecture of Coleman, Kaskel, and Ribet concerning the way in which the modular curve X_{0}(N) intersects the torsion subgroup of its Jacobian when N is prime. In particular we prove their conjecture for all but seven primes N < 500 and establish some results valid for arbitrary values of N.

Publications:

Kamienny’s Criterion and the Method of Coleman and Chabauty, to appear in the Proceedings of the AMS.

We give a new proof of Kamienny’s Criterion (which concerns the uniform boundedness theorem for the torsion on elliptic curves) by applying the method of Coleman and Chabauty to symmetric powers of X_{0}(N).

On the Isomorphism Between the Dualizing Sheaf and the Canonical Sheaf (with János Csirik), submitted to the Proceedings of the AMS.

We give a new proof of the isomorphism between the dualizing sheaf and the canonical sheaf on a nonsingular projective variety over a perfect field. The proof is elegant and number-theoretic in flavor.

Cartier Points on Curves, (in preparation).

A Cartier point on a curve X in characteristic p is a point P such that the hyperplane of regular differentials on X vanishing at P is stable under the Cartier operator. We give some basic properties of Cartier points and as an application generalize a theorem of Ekedahl on superspecial curves.

Trigonal Modular Curves and Torsion Points on X_{0}(N), (in preparation). We determine the exact set of primes N such that X_{0}(N) is trigonal. This has applications to a conjecture of Coleman, Kaskel, and Ribet.

Honors and Awards:

Sloan Dissertation Fellowship in Mathematics  1998-1999
Simons Foundation Scholarship for Excellence in Mathematics 1997
Department of Defense NDSEG Graduate Fellowship  1995-1998
National Security Agency Special Performance Cash Award  1994
Phi Kappa Phi National Fellowship  1994
University of Maryland Regents Scholarship  1990-1994

Work Experience:

National Security Agency Director’s Summer Program 1992,1994

Teaching Experience:

Instructor, Academic Talent Development Program  1995 - 1998
Teaching Assistant, University of California at Berkeley 1994 - 1995

Presentations:

Speaker at AMS Special Session, Regional Meeting in Tucson, AZ, Nov. 14-15, 1998

(Topic: Trigonal Modular Curves) Speaker at AMS Special Session, Joint Mathematics Meeting in San Antonio, Jan. 13-16, 1999

(Topic: Computing Cartier Points) Speaker at AMS Special Session, Region Meeting in Las Vegas, Apr. 10-11, 1999

(Topic: Torsion Points on X_{0}(N))

References:

Prof. Robert Coleman (thesis advisor), University of California at Berkeley Prof. Ken Ribet, University of California at Berkeley Prof. Hendrik Lenstra, University of California at Berkeley Prof. Arthur Ogus, University of California at Berkeley Prof. Barry Mazur, Harvard University Dr. Nina Gabelko, UC Berkeley Academic Talent Development Program