**Permanent faculty and their fields of interests**

Pete L. Clark, *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 Litt, *Assistant Professor, Ph.D. Stanford, 2015.* 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 Lyall, *Professor*, *Ph.D. University of Wisconsin, 2004*. Arithmetic combinatorics and harmonic analysis.

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

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

Paul Pollack,* 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.

Jiuya Wang, *Assistant Professor, Ph.D. University of Wisconsin, 2018*. Algebraic number theory. Arithmetic Statistics. Group Theory. Representation Theory. Distribution of number fields and class groups.

**Emeriti professors**

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

Robert Rumely,* Professor, Ph.D. Princeton, 1978. *Retired from UGA in 2017. Capacity theory, arithmetic intersection theory. Decidability of arithmetic theories. Model-theoretic algebra. Primality testing, primes in arithmetic progressions, zeroes of Dirichlet L-series.

**Post Doctoral Associates and their fields of interest**

Borys Kadets, *Limited Term Assistant Professor,* *Ph.D. MIT, 2020*. Arithmetic geometry. Monodromy and Galois actions in number theory and algebraic geometry. Arithmetic of algebraic curves. Rational points on varieties. Point-count estimates over finite fields.

Padmavathi Srinivasan, *Limited Term Assistant Professor,* *Ph.D. MIT, 2016*. Degenerations of families of curves. Models of curves. Explicit computation of topological, arithmetic and combinatorial invariants of degenerations of curves (conductors, discriminants, Tamagawa numbers). Curves over finite fields and their zeta-functions. Arithmetic enrichments of enumerative problems in algebraic geometry. Field arithmetic.

Nicholas Triantafillou, *Postdoctoral Research and Teaching Associate**, Ph.D. MIT, 2019*. Chabauty-Coleman p-adic method. Kim's nonabelian Chabauty. Integral/rational points on algebraic varieties. Computing zeta functions of algebraic varieties. Selmer group statistics. Covers of curves. Sphere packing.

**47 Recent Graduates and their Dissertations**

*2022*

**Komal Agrawal** (Paul Pollack), *On Some Problems Concerning Integer Recurring Sequences.*

**Arvind Suresh** (Dino Lorenzini), *Realizing Galois Representations in Abelian Varieties by Specialization.*

*2021*

**Matthew Just **(Paul Pollack), *Asymptotic Expansions for some Counting Functions in Group Theory.*

**Mentzelos Melistas **(Dino Lorenzini), *Reduction and Torsion Points of Abelian Varieties.*

**Makoto Suwama **(Dino Lorenzini), *Two Topics in Algebra and Number Theory.*

*2020*

**Kubra Benli **(Paul Pollack), *Three Topics in Analytic Number Theory.*

*2019*

**Noah Lebowitz-Lockard **(Paul Pollack), *The distribution of some special arithmetic functions.*

**Lori Watson** (Pete L. Clark),* Hasse Principle violations in twist families of hyperelliptic and superelliptic curves.*

*2018*

**Marko Milosevic** (Pete L. Clark), *Torsion of elliptic curves. *

*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.*

**Katherine Thompson** (Jonathan Hanke/Daniel Krashen) *Explicit Representation Results of Quadratic Forms Over Q and Q(sqrt(5)). *

*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*.

*1993*

**James Haglund **(R. Canfield), *Compositions, rook placements, and permutations of vectors.*

*1992*

**Renet Lovorn **(C. Pomerance), *Rigorous, Subexponential Algorithms for Discrete Logarithms Over Finite 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*.