Number Theory and
Arithmetic
Geometry Group
Permanent
faculty and their fields of interests.
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 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 cryptography.
Dino Lorenzini,
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. Model-theoretic algebra.
Primality testing, primes in arithmetic progressions, zeroes of
Dirichlet L-series.
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.
Weekly Seminars
Schedule
Number Theory: Mondays at 3:30.
Arithmetic Geometry: Wednesdays at 3:30.
Algebraic Geometry: Tuesdays, 3:30-5:00.
VIGRE
In 2001-2002,
Andrew Granville organized a VIGRE research group on Prime number races.
Members of the group were Jim Solazzo,
Zubeyir Cinkir, Brian Lawler,
Michael Guy,
Mike Beck,
and Eric Pine.
In 2002-2003,
Dino Lorenzini organizes a VIGRE research group on the rank of an elliptic curve.
Members of the group to be announced.
More
information on VIGRE at UGA
Recent graduates and
their dissertation.
Gang Yu (C. Pomerance), Average size of the 2-Selmer
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 p-divisibility 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 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 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 .
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'.
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