
Number Theory and Arithmetic Geometry Group

Permanent faculty and their fields of interests.
William Alford,
Associate Professor, Ph.D. Tulane, 1963. Factoring and other number theory problems by computer.
Matthew Baker,
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.
Sybilla Beckmann,
Associate Professor, Ph.D. U. Penn., 1986.
Galois theory.
The inverse galois problem, that is, to determine whether every finite
group
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.
Andrew Granville,
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.
Dan Lieman,
Associate Professor, Ph.D. Brown, 1992.
Special values of Lseries, Fourier coefficients of metaplectic forms,
analytic theory of automorphic and metaplectic forms, exponential sums,
sparse polynomials and cryptography, applications of number theory to
cryptography.
Dino Lorenzini,
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.
Robert Rumely,
Professor, Ph.D. Princeton, 1978.
Capacity theory, arithmetic intersection theory.
Decidability of arithmetic theories. Modeltheoretic algebra.
Primality testing, primes in arithmetic progressions,
zeroes of Dirichlet Lseries.
Postdoctoral Associates and their fields of interests.
Stephen Astels,
Ph.D. University of Waterloo, 1999. Cantor sets & continued
fractions. Distributions of large primes. Squarefree numbers and
squarefree parts of numbers.
Nathan Ng,
Ph.D. University of British
Columbia, 2000.
Riemann zeta function. Zeroes of Lfunctions.
Random matrix theory. Prime numbers.
Tom Tucker,
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,
Elham Izadi,
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 2Selmer
group of certain elliptic curves over Q
(2000).
Mark Watkins (C. Pomerance), Class Numbers of Imaginary
Quadratic Fields (2000).
Dina Khalil (A. Granville), On the pdivisibility of class numbers of
quadratic fields
(2000).
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
(1998).
David Penniston (D. Lorenzini), The unipotent part of the generalized jacobian of a curve (1998).
Glenn Fox (A. Granville), A padic Lfunction 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 wellknown
Erdos problem
.
The research of Ernest Croot III is featured in
Fractions to Make Egyptian Scribe Blanch,
Science,
vol 278, 10/10/1997.
The research of Pam Cutter is featured in a May 31st, 1997, article
in
Science News .
The research of Jon Grantham is featured in a June 13th,
1997,
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
Mathematics department
and the web pages of our
other research groups. Our
Graduate Bulletin
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'.
