Number Theory and Arithmetic Geometry Group
Permanent faculty and their fields of interests.
Associate Professor, Ph.D. Tulane, 1963. Factoring and other number theory problems by computer.
Assistant Professor, Ph.D. U.C. Berkeley, 1999.
Galois actions on torsion points. Modular curves and
their Jacobians. Discreteness problems for arithmetic heights.
Linear series and vector bundles in characteristic p.
Arithmetic of curves and their Jacobians.
Associate Professor, Ph.D. U. Penn., 1986.
The inverse galois problem, that is, to determine whether every finite
is the galois group of some extension of the rational numbers.
Arithmetic information on branched coverings, such as fields of
definition. Tilings of the plane. Mathematics education.
Barrow Professor, Ph.D. Queens,1987.
Distribution of primes. Sieving intervals.
Distribution of `smooth' numbers. Properties of binomial coefficients.
Cyclotomic fields. Carmichael numbers. Exponential sums.
Integer solutions to Diophantine equations. Binary quadratic forms and the elementary theory
of elliptic curves. Questions related to factoring and primality testing.
Symbolic computation and `computing by homomorphisms'.
Computational complexity, particularly lower bounds. Power series and the
combinatorics of coefficients. Counting lattice points.
Associate Professor, Ph.D. Brown, 1992.
Special values of L-series, Fourier coefficients of metaplectic forms,
analytic theory of automorphic and metaplectic forms, exponential sums,
sparse polynomials and cryptography, applications of number theory to
Associate Professor, Ph.D. U.C. Berkeley, 1988.
Rational torsion points on abelian varieties. Groups of components
of Néron models
of abelian varieties. Modular curves and their
jacobians. Degenerations of curves.
Monodromy transformations associated to families of curves.
Professor, Ph.D. Princeton, 1978.
Capacity theory, arithmetic intersection theory.
Decidability of arithmetic theories. Model-theoretic algebra.
Primality testing, primes in arithmetic progressions,
zeroes of Dirichlet L-series.
Postdoctoral Associates and their fields of interests.
Ph.D. University of Waterloo, 1999. Cantor sets & continued
fractions. Distributions of large primes. Square-free numbers and
square-free parts of numbers.
Ph.D. University of British
Riemann zeta function. Zeroes of L-functions.
Random matrix theory. Prime numbers.
Ph.D. U.C. Berkeley, 1998. Diophantine approximation. Algebraic points on varieties.
Algebraic Geometry Group.
Our number theory group is complemented by a large
group in algebraic geometry, including Valery Alexeev, William Graham,
Roy Smith, and Robert Varley. For more information, look up the Geometry Group.
Number Theory: Mondays at 3:30.
Arithmetic Geometry: Wednesdays at 3:30.
Algebraic Geometry: Wednesdays at 2:20.
Recent graduates and their dissertation.
Gang Yu (C. Pomerance), Average size of the 2-Selmer
group of certain elliptic curves over Q
Mark Watkins (C. Pomerance), Class Numbers of Imaginary
Quadratic Fields (2000).
Dina Khalil (A. Granville), On the p-divisibility of class numbers of
Pamela Cutter (A. Granville), Finding Prime Pairs with Particular Gaps
and Squarefree Parts of Polynomials (2000).
Ernest Croot III (A. Granville), Unit fractions (2000).
Shuguang Li (C. Pomerance), On Artin's conjecture for composite moduli
David Penniston (D. Lorenzini), The unipotent part of the generalized jacobian of a curve (1998).
Glenn Fox (A. Granville), A p-adic L-function of Two Variables (1997).
Jon Grantham (C. Pomerance), Frobenius Pseudoprimes (1997).
Kevin James (A. Granville), On Congruences for the Coefficients of Modular Forms and Applications (1997).
Ronnie Burthe (C. Pomerance), The Average Witness is 2 (1995).
Fred Cheng (C. Pomerance), An Explicit Upper Bound for the Zeta Function in the Critical Strip (1995).
Anitha Srinivasan (A. Granville), Computations of Class Numbers of Quadratic Fields (1995).
Graduate students in the news.
Ernest Croot III solves well-known
The research of Ernest Croot III is featured in
Fractions to Make Egyptian Scribe Blanch,
vol 278, 10/10/1997.
The research of Pam Cutter is featured in a May 31st, 1997, article
Science News .
The research of Jon Grantham is featured in a June 13th,
article in the
Christian Science Monitor .
Good news: our graduate program in number theory is ranked 10th by
US News and World Report .
You may access from here the University of Georgia
and the web pages of our
other research groups. Our
with information for prospective graduate students is also available
on line. If you are interested in graduate studies in number theory
and would like further information on our group, do not hesitate
to contact any of us.
You should check out Keith Matthews' excellent
Number Theory Web site, for lots of
information on the `Queen of Mathematics'.