Permanent faculty and their fields of interests

Benjamin BakkerAssistant Professor, Ph.D. Princeton University, 2010.  Geometric and arithmetic aspects of hyperbolicity in moduli spaces.  Torsion structures on abelian varieties.  Moduli of sheaves on curves and K3 surfaces.  Birational geometry of hyperkahler varieties.  Derived categories.

Pete L. ClarkProfessor, 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, Adjunct 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.

Daniel LittAssistant Professor, Ph.D. Stanford, 2015. (On leave at the IAS in 2018-2019.)  Interactions between algebraic and arithmetic geometry. Mixed Hodge structures and Galois actions on fundamental groups of algebraic varieties; iterated integrals and p-adic iterated integrals. Rational points on algebraic varieties. Positivity and vanishing theorems.

Dino Lorenzini, Distinguished Research Professor, Ph.D. U.C. Berkeley, 1988. Rational points on algebraic varieties. Torsion points on abelian varieties. Néron models of abelian varieties. Modular curves and their jacobians. Models of curves and wild ramification. Wild quotient singularities of surfaces.

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

Akos Magyar, Professor, Ph.D. Princeton, 1996. Discrete harmonic analysis. Arithmetic combinatorics. Analytic methods for diophantine problems.

Giorgis PetridisAssistant Professor, Ph.D. University of Cambridge, 2011. Arithmetic combinatorics and their application to exponential sums. Random graphs.

Paul Pollack, Associate 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 Schneider, Lecturer, Ph.D. Emory, 2018. Partition theory; q-series; mock modular and quantum modular forms. Analytic number theory; prime distribution; arithmetic functions; L-functions. Statistical physics; computational chemistry. History of mathematics. Mathematics and music.

Emeriti professors

Carl Pomerance, Distinguished Research Professor, Ph.D. Harvard, 1972. Retired from UGA in 1999.

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. Retired from UGA in 2017.

Post Doctoral Associates and their fields of interest

Brandon Hanson, Limited Term Assistant Professor, Ph.D. University of Toronto, 2015. Analytic number theory. Distribution of solutions to diophantine equations. Additive Combinatorics. Harmonic analysis. Combinatorial geometry.

Raju KrishnamoorthyLimited Term Assistant Professor, Ph.D. Columbia, 2016. Shimura curves, abelian varieties, I-adic local systems, overconvergent F-isocrystals.

Nikon KurnosovPostdoctoral Research and Teaching Associate, Ph.D. Department of mathematics, Higher School of Economics, Moscow, 2016. Geometry of hyperkähler manifolds. Cohomology of hyperkähler manifolds. Automorphisms of complex manifolds. Calabi-Yau manifolds and mirror symmetry.

Recent graduates and their dissertations

2017

Hans D. Parshall (Neil Lyall/Akos Magyar), Point configurations over finite fields.

2016

Jacob Hicks (Pete L. Clark), Quadratic forms over Hasse domains: finiteness of the Hermite constant.

Ken Jacobs (Robert Rumely), Asymptotic behavior of arithmetic equivariants in non-archimedean dynamics.

Lee Troupe (Paul Pollack), Three applications of sieve methods in analytic number theory.

2015

Allan Lacy Mora (Pete L. Clark), On the index of genus one curves.

2014

John Doyle (Robert Rumely), Dynamics of quadratic polynomials over quadratic fields.

2013

David Krumm (Dino Lorenzini), Quadratic points on modular curves.

2012

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 metrized graphs.

2006

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), On the arithmetic of twists 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 triangles into integer lattices.

Milton Nash (R. Rumely), Special values of Hurwitz zeta functions and 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

Stephen Donnelly (R. Rumely), Finding 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.

 

The first doctoral degrees in mathematics at the University of Georgia were awarded in 1951, and one of them was in number theory.

1951

William D. Peeples (G. Huff), Elliptic curves and rational distance sets.