**Single-author published research articles by RTG graduate students**

* 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.

* 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 McFaddin, The 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, to appear in Trans. AMS.

* Hans Parshall, Simplices 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.

* 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 Troupe, Orders 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**

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

* Natalie Hobson, Conformal 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)

* Mentzelos Melistas, * Purely additive reduction of abelian varieties with torsion, preprint (2021)

* Nolan Schock, Intersection theory of the stable pair compactification of the moduli space of six lines in the plane*, preprint (2020)

* Luca Schaffler, The KSBA compactification of the moduli space of D_{1,6}-polarized Enriques surfaces*, preprint (2016)

* Arvind Suresh, Constructing curves of high rank via composite polynomials,* 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**

** Eiichi Bannai, Etsuko Bannai, Ziqing Xiang, Wei-Hsuan Yu and Yan Zhu**,

*Classification 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.

* 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.

* Matthew Just and Noah Lebowitz-Lockard, On factorizations into coprime parts,* accepted in Int. J. Number Theory

* 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**

* 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)

* Pete L. Clark, Tyler Genao, and Freddy Saia, Chevalley-Warning at the boundary*, preprint (2020)

* Pete L. Clark, Tyler Genao, Paul Pollack, and Freddy Saia, The least degree of a CM point on a modular curve*, preprint (2019)

* 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).

**Published articles with RTG postdocs and other RTG members**

* 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 Giansiracusa, Modular 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 unity**, **to appear in Proc. Lond. Math. Soc.(3).

* Ben Lund and Giorgis Petridis, Bisectors and distances, *Discrete 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**

**Brandon Hanson and Giorgis Petridis**, A question of Bukh on sums of dilates, preprint (2021)

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**RTG Dissertations**

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* 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 constant, *2016

* 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

* 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*

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