Single-author published research articles by RTG graduate students (28)


Kübra Benli, On the number of pure fields of prime degree, Colloquium Mathematicum 153(1) (2018), 39-50.

Kübra Benli, Small prime k-th power residues,  Proc. Amer. Math. Soc. 148 (2020), no. 9, 3801–3809.

Kübra Benli, On the number of prime factors of the composite numbers resulting after a change of digits of primes, J. Théor. Nombres Bordeaux 31 (2019), no. 3, 689–696.

Tyler Genao, Typically bounding torsion on elliptic curves with rational j-invariant, To appear in Journal of Number Theory

William Hardesty, Support varieties of line bundle cohomology groups for SL3 (k), J. Algebra 448 (2016), 127-173.

William Hardesty, On support varieties and the Humphreys conjecture in type A, Adv. Math. 329 (2018), 392-421.

Natalie Hobson, Quantum Kostka and the rank one problem for sl_2m, Adv. Geom. 19 (2019), no. 1, 71–88.

Kenneth Jacobs, Equidistribution of the crucial measures in non-Archimedean dynamics, J. Number Theory 180 (2017), 86–138.

Kenneth Jacobs, Quantitative logarithmic equidistribution of crucial measures, Research in Number Theory, 4(1) (2018), 1-10.

Kenneth Jacobs, Lower bounds for non-archimedean Lyapunov exponents,  Trans. Amer. Math. Soc. 371 (2019), no. 9, 6025–6046.

Matthew Just, On upper bounds for the count of elite primes , Integers 20 (2020), Paper No. A76, 5 pp. 11N05.

Noah Lebowitz-Lockard, Domains with properties weaker than atomicity, Comm. Algebra 47 (2019), no. 5, 1862–1868.

Noah Lebowitz-Lockard, Additively unique sets of prime numbers, International Journal of Number Theory, 14:10 (2018), 2757-2765.

Noah Lebowitz-Lockard, The distribution function of a polynomial in additive functions, Ramanujan J. 49 (2019), no. 3, 491–504.

Andrew Maurer, On the finite generation of relative cohomology for Lie superalgebras,  Proc. Amer. Math. Soc. 147 (2019), no. 5, 1897–1910.

Patrick McFaddinThe group of K_1-zero-cycles on the second generalized Severi–Brauer variety of an algebra of index 4, J. Algebra 479 (2017), 192-202.

Mentzelos Melistas, On a conjecture of Agashe, Trans. AMS 374 (2021), no. 10, 7143–7160.

Mentzelos Melistas, Purely additive reduction of abelian varieties with torsion, to appear in J. Number Theory.

Hans ParshallSimplices over finite fields, Proc. Amer. Math. Soc. 145, no. 6 (2017), 2323-2334.

Hans Parshall, Small gaps between configurations of prime polynomials, Journal of Number Theory 162 (2016), 35–53.

Luca Schaffler, On the cone of effective 2-cycles on M-Bar _ {0, 7}, European Journal of Mathematics, Volume 1, Issue 4 (2015), 669-694.

Luca Schaffler, K3 surfaces with Z_2^2 symplectic action, Rocky Mountain J. Math. 48 (2018), no. 7, 2347–2383.

Luca SchafflerThe KSBA compactification of the moduli space of D_{1,6}-polarized Enriques surfaces, Math. Zeit. 300 (2022), 1819–1850.

Nolan Schock Intersection theory of the stable pair compactification of the moduli space of six lines in the plane, European J. of Math. 8 (2022), 139–192.

Lee Troupe, On the number of prime factors of values of the sum-of-proper-divisors function, J. Number Theory 150C (2015), 120-135.

Lee Troupe, Bounded gaps between prime polynomials with a given primitive root, Finite Fields Appl. 37, (2016), 295–310.

Lee TroupeOrders of reductions of elliptic curves with many and few prime factors, Int. J. Number Theory 13, no. 8 (2017), 2115–2134.

Ziqing Xiang, Nonexistence of nontrivial tight 8-designs, J. Algebraic Combin. 47, no. 2 (2018), 301–318.


Single-author preprints by RTG graduate students (9)


Tyler Genao, Typically bounding torsion on elliptic curves isogenous to rational j-invariant, preprint (2021)

Natalie HobsonConformal blocks in type C at level one (2016)

Matthew Just, Compositions that are palindromic modulo m, preprint (2021)

Matthew Just, Numbers which are only orders of abelian or nilpotent groups, preprint (2021)

Noah Lebowitz-Lockard, Irreducible quadratic polynomials and Euler’s function, preprint (2018)

Nolan SchockQuasilinear tropical compactifications, preprint (2022)

Arvind Suresh, Constructing curves of high rank via composite polynomials, preprint (2021)

Makoto Suwama, On Trace 0 Matrices and Commutators, preprint (2021)

Matthew Zawodniak, A moduli space for rational homotopy types with the same homotopy Lie algebra, preprint (2015)


Published articles with RTG graduate student authors (25)


Eiichi Bannai, Etsuko Bannai, Ziqing Xiang, Wei-Hsuan Yu and Yan ZhuClassification of Spherical 2-distance {4,2,1}-designs by Solving Diophantine Equations, Taiwanese J. Math. 25 (2021), no. 1, 1–22.

Kübra Benli and Paul Pollack, Small prime kth power residues for k=2,3,4: A reciprocity laws approach, Proc. Amer. Math. Soc. 147 (2019), 987-994.

Adrian Brunyate and Pete L. Clark, Extending the Zolotarev-Frobenius approach to quadratic reciprocity, Ramanujan J. 37 (2015), 25–50.

A. Caminata, N. Giansiracusa, H-B. Moon, and L. Schaffler, Equations for point configurations to lie on a rational normal curve, Advances in Mathematics 340 (2018), 653–683.

Pete L. Clark, Saurabh Gosavi, and Paul Pollack, The number of atoms in a primefree atomic domain, Comm. Algebra 45 (2017), 5431–5442.

Pete L. Clark and Allan Lacy, There are genus one curves of every index over every infinite, finitely generated field, J. reine angew. Math. 749 (2019), 65–86.

Pete L. Clark, Noah Lebowitz-Lockard, and Paul Pollack, A Note on Golomb topologies, Quaest. Math. 42 (2019), no. 1, 73–86.

Pete L. Clark, Marko Milosevic, and Paul Pollack, Typically bounding torsion, J. Number Theory 192 (2018), 150-167.

Pete L. Clark and Lori Watson, ABC and the Hasse principle for quadratic twists of hyperelliptic curves  C.R. Math. Acad. Sci. Paris 356 (2018), 911-915.

Pete L. Clark and Lori Watson, Varga's theorem in number fields. INTEGERS 18 (2018), A74, 11pp.

Pete L. Clark, Tyler Genao, and Freddy Saia, Chevalley-Warning at the boundary, to appear in Expo. Math.

Pete L. Clark, Tyler Genao, Paul Pollack, and Freddy Saia, The least degree of a CM point on a modular curve, to appear in J. London Math. Soc.

John Doyle, Kenneth Jacobs, and Robert Rumely, Configuration of the crucial set for a quadratic rational map, Res. Number Theory 2 (2016), Art. 11, 16 pp.

William Hardesty, Daniel Nakano, and Paul Sobaje, On the existence of mock injective modules for algebraic groups, Bull. Lond. Math. Soc. 49 (2017), no. 5, 806–817.

Lauren Huckaba, Neil Lyall, and Ákos Magyar, Simplices and sets of positive upper density in R^d, Proc. Amer. Math. Soc. 145, no. 6 (2017), 2335–2347.

L. Andrew Jenkins and Daniel K. Nakano, The nilpotent cone for classical Lie superalgebras, Proc. of the AMS 149 (2021), 5065-5080.

Matthew Just and Noah Lebowitz-Lockard, On factorizations into coprime parts,  Int. J. Number Theory 17 (2021), no. 8, 1825–1850.

Chun-Ju Lai, Daniel K. Nakano, and Ziqing Xiang, On q-Schur algebras corresponding to Hecke algebras of type B , Transformation Groups, (2020).

Noah Lebowitz-Lockard and Paul Pollack, Clustering of linear combinations of multiplicative functions, Journal of Number Theory, 180 (2017), 660–672.

Noah Lebowitz-Lockard and Paul Pollack, On ordered factorizations into distinct parts, Proc. Amer. Math. Soc. 148 (2020), no. 4, 1447–1453.

Dino Lorenzini, Mentzelos Melistas, Arvind Suresh, Makoto Suwama, and Haiyang Wang, Integer dynamics, to appear in Int. J. Number Theory.

Neil Lyall, Ákos Magyar, and Hans Parshall, Spherical configurations over finite fields,  Amer. J. Math. 142 (2020), no. 2, 373–404.

Daniel Nakano and Ziqing Xiang, Support varieties for Hecke algebras, Homology, Homotopy and Applications, 21(1), (2019), 59–82.

Paul Pollack and Lee Troupe, Two problems concerning irreducible elements in rings of integers of number fields, Bull. Aust. Math. Soc. 96, no. 1 (2017), 44–58.

Zhen Cui, Jiacheng Xia, and Ziqing Xiang, Rational designs, Adv. in Math. 352 (2019), 541–571.


Preprints with RTG graduate student authors (6)


K. Agrawal and P. Pollack, Finite sets containing near primitive roots,  preprint (2020)

Jordan Clark and Lori Watson, On generalizations of the Second Euclid-Mullin sequence, preprint (2017)

David Galban and Daniel K Nakano, On sheaf cohomology for supergroups arising from classical simple Lie superalgebras, preprint (2022)

Matthew Just and Paul Pollack, Variations on a theme of Schinzel and Wójcik, preprint (2021)

Matthew Just and M. Schneider, On a divisor of the central binomial coefficient, preprint (2021)

Dino Lorenzini and Ziqing Xiang, Integral points on variable separated curves, preprint (2018)


Articles with RTG undergraduates


Jackson Hopper and Paul Pollack, Digitally delicate primes, J. Number Theory 168 (2016), 247–256.

Matija Bucic, Pat Devlin, Mo Hendon, Dru Horne, and Ben Lund, Perfect matchings and derangements on graphs, J. Graph Theory (2021).


Preprint with RTG undergraduates


A. P. Akande, Tyler Genao, Summer Haag, Maurice D. Hendon, Neelima Pulagam, Robert Schneider, A. V. Sills, Computational study of non-unitary partitions , submitted December 2021.


Published articles with RTG postdocs and other RTG members (11)


Prakash Belkale, Angela Gibney, and Anna Kazanova, Scaling of conformal blocks and generalized theta functions over M_{g,n}_bar, Math. Z. 284 (2016), no. 3-4, 961–987.

Abbey Bourdon, Pete L. Clark, and James Stankewicz, Torsion points on CM elliptic curves over real number fields, Trans. Amer. Math. Soc. 369 (2017), no. 12, 8457–8496. 

Abbey Bourdon, Pete L. Clark, and Paul Pollack, Anatomy of torsion in the CM case, Math. Z. 285 (2017), no. 3-4, 795–820.

Abbey Bourdon and Paul Pollack, Torsion subgroups of CM elliptic curves over odd degree number fields, Int. Math. Res. Not. IMRN (2017), no. 16, 4923–4961.

Patricio Gallardo and Noah GiansiracusaModular interpretation of a non-reductive Chow quotient, Proceedings of the Edinburgh Mathematical Society 61 no. 2 (2018), 457–477.

Brandon Hanson and Giorgis Petridis, Refined estimates concerning sumsets contained in the roots of unityto appear in Proc. Lond. Math. Soc.(3).

Brandon Hanson and Giorgis Petridis, A question of Bukh on sums of dilates, Discrete Analysis, 2021: Paper No. 13, 21 pp.

Ben Lund and Giorgis Petridis, Bisectors and distancesDiscrete Comput. Geom. 64 (2020), no. 3, 995–1012.

Paul Pollack and Joseph Vandehey, Besicovitch, bisection, and the normality of 0.(1)(4)(9)(16)(25) ⋯, Amer. Math. Monthly 122 (2015), no. 8, 757–765.

Paul Pollack and Joseph Vandehey, Some normal numbers generated by arithmetic functions, Canad. Math. Bull. 58 (2015), no. 1, 160–173.

Amber Russell and Laura Rider, Perverse sheaves on the nilpotent cone and Lusztig's generalized Springer correspondence, Lie algebras, Lie superalgebras, vertex algebras and related topics, 273–292, Proc. Sympos. Pure Math. 92, Amer. Math. Soc., Providence, RI, 2016.


Preprints with RTG postdocs and other RTG members


RTG Dissertations (31)


Theresa Brons, Rational and line bundle cohomology for reductive algebraic groups, 2015

Adrian Brunyate, A modular compactification of the space of elliptic K3 surfaces, 2015

Allan Lacy Mora, On the index of genus one curves, 2015

William Dietrich Hardesty, On support varieties for algebraic groups, 2016

Lauren Eileen Huckaba, Simplices and sets of positive upper density in R^d, 2016

Jacob Hicks, Quadratic forms over Hasse domains: finiteness of the Hermite constant2016

Kenneth Scott Jacobs, Asymptotic behavior of arithmetic equivariants in non-archimedean dynamics, 2016

Patrick Kevin McFaddin, K-cohomology of generalized Severi-Brauer varieties, 2016

Lee Thomas Troupe, Three applications of sieve methods in analytic number theory, 2016

Maren Kathaleen Turbow, Structure theory of graded central simple algebras, 2016

Matthew David Zawodniak, A moduli space for rational homotopy types with the same homotopy Lie algebra, 2016

Brian Anthony Bonsignore, Cohomological n-equivalence of differential graded algebras, 2017

Natalie Laura Fleischmann Hobson, Vector bundles of conformal blocks in Types A and C from a combinatorial approach, 2017

Hans David Parshall, Point configurations over finite fields, 2017

Luca Schaffler, The KSBA compactification of a 4-dimensional family of polarized Enriques surfaces, 2017

Marko Milosevic, Torsion of Elliptic Curves, 2018

Noah Lebowitz-Lockard, The distribution of some special arithmetic functions, 2019

Andrew Maurer, Cohomology and support varieties for classical Lie superalgebras, 2019

Lori Watson, Hasse principle violations in twist families of hyperelliptic and superelliptic curves, 2019

Xian Wu, Stable pair compactification of the moduli space of two special families of calabi-yau 3-folds and chow quotients of grassmannians by diagonal subtori, 2019

Ziqing Xiang, Representation theory for Iwahori-Hecke algebras and Schur algebras of classical type, 2019

Kubra Benli, Three Topics in Analytic Number Theory, 2020

Ernest Guico, Admissibility of Finite Groups over Semi-global Fields, 2020

Matthew Just, Asymptotic Expansions for some Counting Functions in Group Theory, 2021

Mentzelos Melistas, Reduction and Torsion Points of Abelian Varieties, 2021

Makoto Suwama, Two Topics in Algebra and Number Theory, 2021

Komal Agrawal, , 2022

L. Andrew Jenkins, , 2022

David Galban, , 2022

Arvind Suresh, , 2022

Nolan Schock, , 2022



To download any other UGA dissertation in pdf form, please search the UGA Electronic Theses and Dissertations