Theory and Arithmetic Geometry Group
faculty and their fields of interests.
Clark, Associate Professor, Ph.D. Harvard 2003. Arithmetic
of abelian varieties; torsion points, endomorphism algebras, Weil-Chatelet
groups. Modular curves and Shimura curves. Period-index problems.
Pointless varieties and the (anti-) Hasse principle. Geometric approaches
to the inverse Galois problem.
Daniel Krashen, Associate Professor, Ph.D University of Texas 2001, Finite dimensional division algebras, quadratic forms, and their interplay with algebraic groups and homogeneous varieties. Algebraic cycles and motives. Moduli and configuration spaces.
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.
Lyall, Associate Professor, Ph.D., University of
Wisconsin, 2004. Application of Fourier analytic techniques
to problems in additive combinatorics. Discrete problems in harmonic
Paul Pollack, Assistant Professor, Ph.D. Dartmouth, 2008. Classical problems in number theory, with an emphasis on elementary and analytic methods. Arithmetic functions and their iterates; perfect numbers and their relatives. Multiplicative number theory. The number-theoretic work of Paul Erdos.
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
Doctoral Associates and their fields of interest
Lola Thompson, Postdoctoral Associate, Ph.D. Dartmouth, 2012.
Number theory, particularly problems that have an elementary, analytic or combinatorial flavor. Arithmetic of polynomials in Z[x] and F_p[x].
Algebraic Geometry Group
Our number theory group is complemented by a large group in algebraic
geometry, including Valery Alexeev, Angela Gibney, William Graham, Elham Izadi,
Roy Smith, and Robert Varley. For more information, look up the Geometry
Weekly Seminar Schedule
Theory/Arithmetic Geometry: Dino Lorenzini
Wednesday, 3:30p.m., Room 304
Joint Athens-Atlanta Number Theory Seminar
In 2011-2012, Pete L. Clark organized a VIGRE research group on
Whatever Happened to the Geometry of Numbers?
As part of the VIGRE Summer School Training Program, Robert Rumely organized in May 2011 the two-week Summer School Program in Arithmetic Dynamics.
In the fall of 2008, Dino Lorenzini organized an undergraduate IVRG (introductory VIGRE research group) on the Frobenius number. A paper resulted from the IVRG, published in the Journal of Integer Sequences.
In 2007-2008, Pete L. Clark and Patrick Corn organized a VIGRE research group on Computations on CM elliptic curves.
In the Fall of 2007, Dino Lorenzini organized a VIGRE research group on Graphs and Geometry.
In the Fall of 2006, Dino Lorenzini organized a VIGRE research group on the Laplacian of a graph.
In 2005-2006, Robert Rumely organized a VIGRE research group on the Riemann-Siegel Formula.
During the summer of 2005, Akos Magyar ran an REU
on Ramsey theory.
In 2004-2005, Dino Lorenzini organized a VIGRE research group on ranks of curves. Members of the group are: Robert
Brice, Sungkon Chang, Jerry Hower, Jacob Keenum, Nausheen Lotia,
Daeshik Park, Clay Petsche, Charles Pooh, Dong Hoon Shin, and Juhyung
During the summer of 2003, Matt Baker and Robert Rumely ran an REU on Analysis on Metrized Graphs.
In 2002-2003, Dino Lorenzini organized a VIGRE research group
on the rank of an elliptic curve. Members of the group are:
Bill Rulla, Sungkon Chang, Zubeyir Cinkir, Steven Donnelly, Zach
Michaels, Charles Pooh, Joe Rusinko, Rene Shumbusho.
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.
information on VIGRE at UGA
Recent graduates and their dissertation.
Alex Rice (Neil Lyall), Improvements and Extensions of Two Theorems of Sarkozy.
James Stankewicz (Pete L. Clark/Dino Lorenzini), Twists of Shimura Curves.
Nathan Walters (Robert Rumely), Some Capacity-Theoretic Results Extended to Algebraic Curves.
Jeremiah Hower (Dino Lorenzini), On elliptic curves and arithmetical graphs.
Zubeyir Cinkir (Robert Rumely), The tau constant of a metrized graph.
Daeshik Park (Robert Rumely), The Fekete-Szego
Theorem with Splitting Conditions on the Projective Line of Positive
Paulo Almeida (A. Granville), Sign Changes
of Error Terms Related to Certain Arithmetic Functions.
Sungkon Chang (D. Lorenzini), The arithmetic of
twists of the jacobians of superelliptic curves.
Charles Pooh (R. Rumely), Capacity theory
and Algebraic integers.
Michael Beck (A. Granville), Square Dependence in Random
Jim Blair (A. Magyar), On the Embedding
of Simplicies into Integer Lattices.
Milton Nash (R. Rumely), Special Values of
Dirichlet L- functions.
Eric Pine (A. Granville), Sums of Integer Cubes.
Rene-Michel Shumbusho (D. Lorenzini), Elliptic
Curves With Prime Conductor and a Conjecture of Cremona.
Steve Donnelly (R. Rumely), Elements of given order in
Tate-Shafarevich groups of elliptic curves.
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
Dina Khalil (A. Granville), On the p-divisibility of class
numbers of quadratic fields.
Pamela Cutter (A. Granville), Finding Prime Pairs with
Particular Gaps and Squarefree Parts of Polynomials.
Ernest Croot III (A. Granville), Unit fractions.
Shuguang Li (C. Pomerance), On Artin's conjecture for
David Penniston (D. Lorenzini), The unipotent part of
the generalized jacobian of a curve.
Glenn Fox (A. Granville), A p-adic L-function of Two Variables.
Jon Grantham (C. Pomerance), Frobenius Pseudoprimes.
Kevin James (A. Granville), On Congruences for the Coefficients
of Modular Forms and Applications.
Ronnie Burthe (C. Pomerance), The Average Witness is 2.
Fred Cheng (C. Pomerance), An Explicit Upper Bound for
the Zeta Function in the Critical Strip.
Anitha Srinivasan (A. Granville), Computations of Class
Numbers of Quadratic Fields.
Graduate students in the news
- Ernest Croot III solves well-known Erdos
The research of Ernest Croot III is featured in Fractions to
Make Egyptian Scribe Blanch, Science, vol
- The research of Pam Cutter is featured in a May 31st, 1997, article
- The research of Jon Grantham is featured in a June 13th, 1997, article
in the Christian Science Monitor.
Three theses in number theory won UGA
award for best thesis of the year.
Two theses in number theory won a UGA Dissertation Completion Award: James Stankewicz (2011-2012), and David Krumm (2012-2013).
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'.
last updated: NOVEMBER 28, 2012