Department of Mathematics at the University of Georgia

Permanent faculty and their fields of interests.

Pete L. 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.

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.

Neil Lyall, Associate Professor, Ph.D., University of Wisconsin, 2004. Application of Fourier analytic techniques to problems in additive combinatorics. Discrete problems in harmonic analysis.

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 Dirichlet L-series.

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 Group.

Weekly Seminar Schedule

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 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.

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 Yi.

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.

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.

2009

Jeremiah Hower (Dino Lorenzini), On elliptic curves and arithmetical graphs.

2007

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 Characteristic p.

2005

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.

2004

Michael Beck (A. Granville), Square Dependence in Random Integers.
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.

2003

Steve Donnelly (R. Rumely), Elements of given order in Tate-Shafarevich groups of elliptic curves.

2000

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.
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.

1998

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.

1997

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.

1995

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.

Two theses in number theory won a UGA Dissertation Completion Award: James Stankewicz (2011-2012), and David Krumm (2012-2013).

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.