**Single-author published research articles by RTG graduate students (30)**

**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**, *J. Number Theory 238 (2022), 823–841.

**Tyler Genao**,* Typically bounding torsion on elliptic curves isogenous to rational j-invariant,* Proc. Amer. Math. Soc. 151 (2023), no. 5, 1907–1914.

**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, 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 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.

**Luca Schaffler**, *The 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.

**Makoto Suwama**, *On Trace Zero Matrices and Commutators,* J. of Algebra (2023)

**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 (9)**

**Tyler Genao**,* Polynomial bounds on torsion from a fixed geometric isogeny class,** (2022)*

**Tyler Genao**,* Growth of torsion groups of elliptic curves upon base change from number fields,** (2022)*

**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)

**Nolan Schock**, *Quasilinear tropical compactifications*, preprint (2022)

**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 (27)**

* A. P. Akande, and Robert Schneider, Semi-modular forms from Fibonacci-Eisenstein series,* Ramanujan J. 60 (2023), no. 1, 59–68.

* 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.

**Pete L. Clark, Tyler Genao, and Freddy Saia, ***Chevalley-Warning at the boundary*, Expo. Math. 39 (2021), no. 4, 604--623.

**Pete L. Clark, Tyler Genao, Paul Pollack, and Freddy Saia, ***The least degree of a CM point on a modular curve*, J. London Math. Soc. (2) 105 (2022), no. 2, 825--883.

**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.

**Matthew Just and M. Schneider**, *On a divisor of the central binomial coefficient,** *to appear in Ramanujan J.

**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 (5)**

**Preprints with RTG graduate student authors (5)**

**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)*

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

* *

**Articles with RTG undergraduates**

**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).*

** Akande, A. P.; Genao, Tyler; Haag, Summer; Hendon, Maurice D.; Pulagam, Neelima; Schneider, Robert; Sills, Andrew V., **Computational study of non-unitary partitions, J. Ramanujan Math. Soc. 38 (2023), no. 2, 121–128.

* *

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

**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 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).

**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 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**

**Preprints with RTG postdocs and other RTG members**

* *

**RTG Dissertations (34)**

**RTG Dissertations (34)**

**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*

**Komal Agrawal**, *On Some Problems Concerning Integer Recurring Sequences**, 2022*

**David Galban**, *Cohomology and Representation Theory for Lie Superalgebras **, 2022*

**L. Andrew Jenkins**, *The Nilpotent Cone for Classical Simple Lie Superalgebras**, 2022*

**Nolan Schock**, *Geometry of Tropical Compactifications of Moduli Spaces**, 2022*

**Arvind Suresh**, *Realizing Galois Representations in Abelian Varieties by Specialization**, 2022*

**Tyler Genao, **Typical and Polynomial Bounds on Torsion of Elliptic Curves, and Torsion Upon Base Change**, **2023

**Freddy Saia, **A Volcanic Approach to CM Points on Shimura Curves, 2023

* Jack Wagner, On the Category of Exotic Coherent Sheaves on Partial Resolutions of the Nilpotent Cone with Connections to the Affine Grassmannian*,

*2023*

* Peter Woolfit, On k-degenerate Distance Graphs in Finite Fields and a Class of 2-degenerate Distance Graphs in the Integer Lattice*,

*2023*

* Patrick Akande, Three results on the distribution of arithmetic functions*,

*2024*

* Haiyang Want, Three topics in Number Theory*,

*2024*

* *

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