Positions Held
University of Illinois
Fall 2008–Spring 2011
J. L. Doob Research Assistant Professor / NSF Postdoctoral Fellow
Institute for Advanced Study
Fall 2009
Member of the School of Mathematics
Dartmouth College
Spring 2010
Visiting Research Scholar
University of British Columbia / Simon Fraser University
July 2011–April 2012
Postdoctoral Fellow
University of Georgia
- Assistant Professor — Fall 2012–Summer 2016
- Associate Professor — Fall 2016–Summer 2017; with tenure, Fall 2017–Summer 2020
- Professor — Fall 2020–present
- Director of Graduate Studies, Mathematics — Fall 2025–present
Education
University of Georgia
Spring 2003
Bachelor of Science, Mathematics
Princeton University
Fall 2003–Winter 2005
Dartmouth College
June 2007
Master of Arts, Mathematics
Dartmouth College
June 2008
Ph.D., Mathematics
Thesis: Prime polynomials over finite fields
Honors and Awards
Fellow of the American Mathematical Society
2025–present
Inducted 2025. “The Fellows of the American Mathematical Society program recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics.”
Lamar Dodd Creative Research Award
2024
Given by the University of Georgia Research Foundation to “recognize an outstanding body of nationally and internationally recognized scholarly or creative activities in the sciences.”
UGA Teaching Academy member
2022–present
Inducted Fall 2022. The Teaching Academy, supported by the Office of Instruction, exists “as a forum to discuss, celebrate and promote teaching excellence.”
Russell Award for Excellence in Undergraduate Teaching
2022
University-wide award recognizing excellence in undergraduate instruction by faculty members in their early academic careers.
NSF Algebra and Number Theory Award DMS-2001581
2020–2023
Statistical Questions in Number Theory and Arithmetic Geometry (award amount $168,000). Currently on a no-cost extension.
Honorific member of the Carrera Nacional de Investigadores en Ciencia
Since 2019
The Carrera Nacional de Investigadores en Ciencia, of the Dominican Republic, is a government initiative with the goal of drawing attention to those who have dedicated their life to research in science, technology, and innovation.
Sandy Beaver Excellence in Teaching Award
2018
Award given each year to honor UGA Franklin College faculty members showing “sustained commitment to high-quality instruction”.
NSF Algebra and Number Theory Award DMS-1402268
2014–2019
Statistical problems in elementary, analytic, and algebraic number theory (award amount $130,925).
NSF Algebra and Number Theory Award DMS-1502336
Summer 2015
(co-PI with L. Thompson, R. Rumely, and G. Yu) Conference grant for “Elementary, analytic, and algorithmic number theory: Research inspired by the mathematics of Carl Pomerance” (award amount $19,728).
NSA Conference Award
Summer 2015
(co-PI with L. Thompson, R. Rumely, and G. Yu) “Carl Pomerance 70th birthday conference” (award amount $15,788).
Recent Invited Addresses
2020 AMS Fall Southeastern Sectional Meeting; special session on “Coding Theory, Cryptography, and Number Theory”
October 2020
Talk: “Thoughts on the order of a mod p”
Luxembourg Number Theory Seminar
October 2020
Talk: “Thoughts on the order of a mod p”
Kansas State Number Theory Seminar
March 2021
Talk: “Multiplicative orders mod p”
Nancy-Metz Number Theory Seminar
April 2021
Talk: “Multiplicative orders mod p”
Combinatorial and Additive Number Theory (CANT) 2021
May 2021
Talk: “Multiplicative orders mod p”
Combinatorial and Additive Number Theory (CANT) 2022
May 2022
Talk: “Equidistribution and weak equidistribution for some arithmetic functions”
LSU Number Theory Seminar
October 2022
Talk: “Some distribution problems concerning arithmetic functions”
2023 Joint Meetings; Budapest Semesters in Math. Special Session
January 2023
Talk: “The frequency of partially perfect numbers”
Math Department Colloquium, Dartmouth College
September 2023
Talk: “Unique factorization: what not everyone knows”
Number Theory Web Seminar
February 2024
Talk: “Stretching, the truth about unique factorization”
AMS-UMI meeting; special session on “The Ideal Theory and Arithmetic of Rings, Monoids, and Semigroups”
July 2024
Talk: “Elasticity of orders in quadratic number fields”
Winter 2024 Canadian Math. Soc. Meeting; special session “Celebrating Greg Martin”
November 2024
Talk: “Counting primes with a given primitive root, uniformly”
2025 Joint Math Meetings, special session for the Budapest Semesters in Mathematics
January 2025
Talk: “How nonunique is your factorization?”
2025 Integers Conference
May 2025
Talk: “How nonunique is your factorization?”
U. Waterloo Number Theory Seminar
June 2025
Talk: “How nonunique is your factorization?”
Purdue Colloquium
September 2025
Talk: “Two thousand years of summing divisors”
Purdue Number Theory Seminar
October 2025
Talk: “How nonunique is your factorization?”
Butler University Colloquium
October 2025
Talk: “Two thousand years of summing divisors”
Accepted Papers
152 numbered publications plus 1 review item.
An explicit approach to Hypothesis H for polynomials over a finite field
2008
The anatomy of integers. Proceedings of a conference on the anatomy of integers, Montreal, March 13th-17th, 2006. Editors: J.M. de Koninck, A. Granville and F. Luca, pp. 259–273
On a conjecture of Beard, O’Connell and West concerning perfect polynomials
2008
(joint with L. Gallardo and O. Rahavandrainy) Finite Fields and their Applications 14, 242–249
A polynomial analogue of the twin prime conjecture
2008
Proc. Amer. Math. Soc. 136, 3775–3784
Simultaneous prime specializations of polynomials over finite fields
2008
Proc. London Math. Soc. 97, 545–567
Arithmetic properties of polynomial specializations over finite fields
2009
Acta Arith. 136, 57-79
On the distribution of sociable numbers (w/ M. Kobayashi and C. Pomerance)
2009
J. Number Theory 129, 1990-2009
A remark on sociable numbers of odd order
2010
J. Number Theory 130, 1732–1736
Revisiting Gauss’s analogue of the prime number theorem for polynomials over a finite field
2010
Finite Fields and their Applications 16, 290-299
Hypothesis H and an impossibility theorem of Ram Murty
2010
Rend. Sem. Mat. Univ. Pol. Torino 68, 183–197
Multiperfect numbers with identical digits (joint with F. Luca)
2011
J. Number Theory 131, 260–284
On polynomial rings with a Goldbach property
2011
Amer. Math. Monthly 118, 71–77
On Dickson’s theorem concerning odd perfect numbers
2011
Amer. Math. Monthly 118, 161–164
Long gaps between deficient numbers
2011
Acta Arith. 146, 33–42
On Hilbert’s solution of Waring’s problem
2011
Cent. Eur. J. Math. 9, 294–301
Powerful amicable numbers
2011
Colloq. Math. 122, 103–123
Values of the Euler and Carmichael functions which are sums of three squares
2011
Integers 11, article A13, 16 pages (electronic)
On some friends of the sociable numbers
2011
Monatsh. Math. 162, 321–327
The greatest common divisor of a number and its sum of divisors
2011
Michigan Math. J. 60, 199–214
Perfect numbers with identical digits
2011
Integers 11A. Proceedings of the Integers Conference 2009. Article 18, 11 pages (electronic)
Quasi-amicable numbers are rare
2011
J. Integer Sequences 14, article 11.5.2, 13 pages (electronic)
The exceptional set in the polynomial Goldbach problem
2011
Int. J. Number Theory 7, 579–591
The Möbius transform and the infinitude of primes
2011
Elem. Math. 66, 118–120
Remarks on a paper of Ballot and Luca concerning prime divisors of a^f(n) − 1
2011
New York J. Math 17, 553–567
On common values of ϕ(n) and σ(m), I (joint with K. Ford)
2011
Acta Math. Hungarica 133, 251–271
Two remarks on iterates of Euler’s totient function
2011
Arch. Math. 97, 443–452
An arithmetic function arising from Carmichael’s conjecture (w/ F. Luca)
2011
J. Théor. Nombres Bordeaux 23, 697–714
The average least quadratic nonresidue modulo m and other variations on a theme of Erdős
2012
J. Number Theory 132, 1185–1202
On the parity of the number of multiplicative partitions and related problems
2012
Proc. Amer. Math. Soc. 140, 3793–3803
On perfect and near-perfect numbers (joint with V. Shevelev)
2012
J. Number Theory 132, 3037–3046
Prime-perfect numbers (joint with C. Pomerance)
2012
Integers 12A/special issue in memory of J. L. Selfridge, article A14, 19 pages
Finiteness theorems for perfect numbers and their kin
2012
American Math. Monthly 119, 670–681
How many primes can divide the values of a polynomial? (joint with F. Luca)
2012
Acta Arith. 156, 19–27
On congruences of the form σ(n) ≡a (mod n) (with A. Anavi and C. Pomerance)
2012
Int. J. Number Theory 9, 115–124
On common values of ϕ(n) and σ(m), II (joint with K. Ford)
2012
Algebra Number Theory 6, 1669–1696
The average least character nonresidue and further variations on a theme of Erdős (joint with G. Martin)
2013
J. London Math. Soc. 87, 22–42
On the degrees of divisors of T^n −1 (joint with L. Thompson)
2013
New York J. Math 19, 91–116
Irreducible polynomials with several prescribed coefficients
2013
Finite Fields and their Applications 22, 70–78
Practical pretenders (joint with L. Thompson)
2013
Publ. Math. Debrecen 82, 651–667
Sets of monotonicity for Euler’s totient function (w/ C. Pomerance and E. Treviño)
2013
Ramanujan J. 30, 379–398
On Mertens’ theorem for Beurling primes
2013
Canad. Math. Bull. 56, 829–843
On the distribution of some integers related to perfect and amicable numbers (joint with C. Pomerance)
2013
Colloq. Math. 30, 169–182
The smallest inert prime in a cyclic number field of prime degree
2013
Math. Res. Lett. 20, 163–179
Paul Erdős and the rise of statistical thinking in elementary number theory (joint with C. Pomerance)
2013
Erdős Centennial, L. Lovász, I. Z. Ruzsa, and V. T. Sós, eds., János Bolyai Math. Soc. and Springer-Verlag, Hungary, 2013, pp. 515–523
Uncertainty principles connected with the Möbius inversion formula (with C. Sanna)
2013
Bull. Aust. Math. Soc. 88, 460–472
Equidistribution mod q of abundant and deficient numbers
2014
Uniform Distribution Theory 9, 99–114
A remark on prime divisors of partition functions
2014
Int. J. Number Theory 10, 125–131
The error term in the count of abundant numbers (joint with M. Kobayashi)
2014
Mathematika 60, 43–65
The smallest prime that splits completely in an abelian number field
2014
Proc. Amer. Math. Soc. 142, 1925–1934
Square values of Euler’s function (joint with C. Pomerance)
2014
Bull. London Math. Soc. 46, 403–414
The primes that Euclid forgot (joint with E. Treviño)
2014
Amer. Math. Monthly 121, 433–437
Variations on a theorem of Davenport concerning abundant numbers (w/ E. Jennings and L. Thompson)
2014
Bull. Aust. Math. Soc. 89, 437–450
Prime splitting in abelian number fields and linear combinations of Dirichlet characters
2014
Int. J. Number Theory 10, 885–903
Averages of the number of points on elliptic curves (w/ G. Martin and E. Smith)
2014
Algebra Number Theory 8, 813–836
Bounded gaps between primes with a given primitive root
2014
Algebra Number Theory 8, 1769–1786
Some arithmetic properties of the sum of proper divisors and the sum of prime divisors
2014
Illinois J. Math 58, 125–147
Euler and the partial sums of the prime harmonic series
2015
Elem. Math. 70, 13–20
Bounded gaps between primes in number fields and function fields (with A. Castillo, C. Hall, R. Lemke Oliver, and L. Thompson)
2015
Proc. Amer. Math. Soc. 143, 2841–2856
An easy generalization of Euler’s theorem on the series of prime reciprocals
2015
American Math. Monthly 122, 159–163
Some normal numbers generated by arithmetic functions (with J. Vandehey)
2015
Canad. Math. Bull. 58, 160–173
The truth about torsion in the CM case (with P. L. Clark)
2015
C. R. Math. Acad. Sci. Paris 353, 683–688
Palindromic sums of proper divisors
2015
Integers 15A/Proceedings of the Erdős Centennial Conference, article A13 (electronic), 12 pages
Harmonious pairs (joint with M. Kozek, F. Luca, and C. Pomerance)
2015
Int. J. Number Theory 11, 1633–1651
Arithmetic functions at consecutive shifted primes (with L. Thompson)
2015
Int. J. Number Theory 11, 1477–1498
The length spectra of arithmetic hyperbolic 3-manifolds and their totally geodesic surfaces (with B. Linowitz and J. S. Meyer)
2015
New York J. Math 21, 955–972
Besicovitch, bisection, and the normality of 0.1491625 . . . (with J. Vandehey)
2015
American Math. Monthly 122, 757–765
Remarks on fibers of the sum-of-divisors function
2015
in Analytic Number Theory: In Honor of Helmut Maier’s 60th Birthday, M. Rassias and C. Pomerance, eds., Springer, 305–320
On relatively prime amicable pairs
2015
Mosc. J. Comb. Number Theory 5, 36–51
The average of the first invariant factor for reductions of CM elliptic curves mod p (with T. Freiberg)
2015
Int. Math. Res. Notices 2015, no. 21, 11333–11350
Some problems of Erdős on the sum-of-divisors function (joint with C. Pomerance)
2016
Trans. Amer. Math. Soc. Ser. B. 3, 1–26
A Titchmarsh divisor problem for elliptic curves
2016
Math. Proc. Cambridge Philos. Soc. 160, 167–189
A remark on divisor weighted sums
2016
Ramanujan J. 40, 63–69
Bounded gaps between primes with a given primitive root, II (w/ R. C. Baker)
2016
Forum Mathematicum 28, 675–687
Digitally delicate primes (w/ J. Hopper)
2016
J. Number Theory 168, 247–256
The representation function for sums of three squares along arithmetic progressions
2016
Proc. Japan Acad., Ser. A Math. Sci. 92, 96–99
An elemental Erdős-Kac theorem for algebraic number fields
2017
Proc. Amer. Math. Soc. 145, 971–987
Extremal primes for elliptic curves with complex multiplication (w/ K. James)
2017
J. Number Theory 172, 383–391
Anatomy of torsion in the CM case (with A. Bourdon and P. L. Clark)
2017
Math. Z. 285, 795–820
Bounds for the first several prime character nonresidues
2017
Proc. Amer. Math. Soc. 145, 2815–2826
A simple proof of a theorem of Hajdu–Jarden–Narkiewicz
2017
Colloq. Math. 147, 217–220
Two problems concerning irreducible elements in rings of integers of number fields (w/ L. Troupe)
2017
Bull. Aust. Math. Soc. 96, 44–58
Counting perfect polynomials (w/ U. Caner Cengiz and E. Treviño)
2017
Finite Fields and their Applications 47, 242–255
Clustering of linear combinations of multiplicative functions (w/ N. Lebowitz-Lockard)
2017
J. Number Theory 180, 660–672
Subgroup avoidance for primes dividing the values of a polynomial
2017
Rocky Mountain J. Math 47, 2043–2050
Numbers divisible by a large shifted prime and large torsion subgroups of CM elliptic curves (w/ N. McNew and C. Pomerance)
2017
Int. Math. Res. Notices 2017, 5525–5553
Torsion subgroups of CM elliptic curves over odd degree number fields (w/ A. Bourdon)
2017
Int. Math. Res. Notices 2017, 4923–4961
Clusters of primes with square-free translates (w/ R. C. Baker)
2017
Revista Mat. Iberoam. 33, 809–829
Bounded gaps between primes and the length spectra of arithmetic hyperbolic 3-orbifolds (w/ B. Linowitz, D. B. McReynolds, and L. Thompson)
2017
C. R. Math. Acad. Sci. Paris 355, 1121–1126
The number of atoms in a primefree atomic domain (w/ P. L. Clark and S. Gosavi)
2017
Comm. Algebra 45, 5431–5442
The truth about torsion in the CM case, II (w/ P. L. Clark)
2017
Quart. J. Math. 68, 1313–1333
Systoles of arithmetic hyperbolic surfaces and 3-manifolds (w/ B. Linowitz, D. B. McReynolds, and L. Thompson)
2017
Math. Res. Lett. 24, 1497–1522
Refinements of Lagrange’s four-square theorem (w/ L. Goldmakher)
2018
Amer. Math. Monthly 125, 258–263
The least prime quadratic nonresidue in a prescribed residue class mod 4
2018
J. Number Theory 187, 403–414
Thue’s lemma in Z[i] and Lagrange’s four-square theorem
2018
Elem. Math. 73, 60–65
Divisor-sum fibers (w/ C. Pomerance and L. Thompson)
2018
Mathematika 64, 330–342
Finding the four squares in Lagrange’s theorem (w/ E. Treviño)
2018
Integers 18A, article A15, 16 pages
Pursuing polynomial bounds on torsion (w/ P. L. Clark)
2018
Israel J. Math. 227, 889–909
A remark on the number field analogue of Waring’s constant g(k)
2018
Math. Nachr. 291, 1893–1898
Waring’s problem for integral quaternions
2018
Indag. Math. 29, 1259–1269
Counting and effective rigidity in algebra and geometry (joint with B. Linowitz, D. B. McReynolds, and L. Thompson)
2018
Invent. Math. 213, 697–758
Typically bounding torsion (w/ P. L. Clark and M. Milosevic)
2018
J. Number Theory 192, 150–167
How often is Euler’s totient a perfect power?
2019
J. Number Theory 197, 1–12
Dirichlet’s proof of the three-square theorem: an algorithmic perspective (w/ P. Schorn)
2019
Math. Comp. 88, 1007–1019
Small prime kth power residues for k = 2, 3, 4: a reciprocity laws approach (w/ K. Benli)
2019
Proc. Amer. Math. Soc. 147, 987–994
A note on Golomb topologies (w/ N. Lebowitz Lockard and P. L. Clark)
2019
Quaestiones Math. 42, 73–86
A note on the least prime that splits completely in a nonabelian Galois number field (w/ Z. Ge and M. Milinovich)
2019
Math. Z. 292, 73–86
Popular subsets for Euler’s φ-function
2019
Math. Ann. 374, 253–271
Eigenvalues of the Laplacian on domains with fractal boundary (w/ C. Pomerance)
2019
Horizons of Fractal Geometry and Complex Dimensions. 2016 Summer School: Fractal Geometry and Complex Dimensions. In celebration of the 60th birthday of Michel Lapidus. R.G. Niemeyer, E.P.J. Pearse, J.A. Rock, T. Samuel, eds., AMS Contemporary Mathematics, vol. 731, 2019.
Symmetric primes revisited (w/ W.D. Banks and C. Pomerance)
2019
Integers 19, article A54, 7 pages
Nonnegative multiplicative functions on sifted sets, and the square roots of −1 modulo shifted primes
2020
Glasgow Math. J. 62, 187–199
Twists of hyperelliptic curves by integers in progressions mod p (w/ D. Krumm)
2020
Acta Arith. 192, 63–71
Reciprocity by resultant in k[t] (w/ P.L. Clark)
2020
L’Enseignement Math. 65, 101–116
On ordered factorizations into distinct parts (w/ N. Lebowitz-Lockard)
2020
Proc. Amer. Math. Soc. 148, 1447–1453
A generalization of the Hardy-Ramanujan inequality and applications
2020
J. Number Theory 210, 171–182
The smallest root of a polynomial congruence
2020
Math. Res. Lett. 27, 43–66
On sums of consecutive triangular numbers (w/ D. Subramaniam and E. Treviño)
2020
Integers 20A. Article A15, 10 pages (electronic)
Phi, primorials, and Poisson (w/ C. Pomerance)
2020
Illinois J. Math. 64, 319–330
Multiplicative partitions of numbers with a large squarefree divisor
2020
Ramanujan J. 53, 595–605
The maximal size of the k-fold divisor function for very large k
2020
J. Ramanujan Math. Soc. 25, 341–345
The reciprocal sum of divisors of Mersenne numbers (w/ Z. Engberg)
2021
Acta Arith. 197, 421–440
Finite sets containing near-primitive roots (w/ K. Agrawal)
2021
J. Number Theory 225, 360–373
Comparing multiplicative orders mod p, as p varies (w/ M. Just)
2021
New York J. Math. 27, 600–614
The number of non-cyclic Sylow subgroups of the multiplicative group modulo n
2021
Canad. Math. Bull. 64, 204–215
A quick route to unique factorization in quadratic orders (w/ N. Snyder)
2021
Amer. Math. Monthly 128, 554–558
The distribution of numbers with many factorizations
2021
Math. Z. 299, 2327–2339
Numbers which are orders only of cyclic groups
2022
Proc. Amer. Math. Soc. 150, 515–524
Joint distribution in residue classes of polynomial-like multiplicative functions (w/ A. Singha Roy)
2022
Acta Arith. 202, 89–104
The least degree of a CM point on a modular curve (w/ P.L. Clark, T. Genao, and F. Saia)
2022
J. London Math. Soc. 105, 825–883
Powerfree sums of proper divisors (w/ A. Singha Roy)
2022
Colloq. Math 168, 287–295
Dirichlet, Sierpiński, and Benford (w/ A. Singha Roy)
2022
J.Number Theory 239, 352–364
On the stable reduction of hyperelliptic curves (w/ C. Gong, Y. Gu, J. Lu)
2022
Tohoku Math. J. 74, 195–213
On Benford’s law for multiplicative functions (w/ V. Chandee, X. Li, and A. Singha Roy)
2023
Proc. Amer. Math. Soc. 151, 4607–4619
Sums of proper divisors follow the Erdős–Kac law (w/ L. Troupe)
2023
Proc. Amer. Math. Soc. 151, 977-988
A problem in comparative order theory (w/ S. Konyagin)
2023
Period. Math. Hung. 86, 24–36
Benford behavior and distribution in residue classes of large prime factors (w/ A. Singha Roy)
2023
Canad. Math. Bull. 66, 626–642
On the greatest common divisor of a number and its sum of divisors, II
2023
Number Theory in Memory of Eduard Wirsing. Helmut Maier, Jörn Steuding, Rasa Steuding, eds. Springer Cham
Intermediate prime factors in specified subsets (w/ N. McNew and A. Singha Roy)
2023
Monatshefte Math. 202, 837–855
Distribution in coprime residue classes of polynomially defined multiplicative functions (w/ A. Singha Roy)
2023
Math. Z. 303, no. 4, paper 93, 20 pages
Two problems on the distribution of Carmichael’s lambda function
2023
Mathematika 69, 1195–1220
The distribution of intermediate prime factors (w/ N. McNew and A. Singha Roy)
2024
Illinois J. Math. 68, 537–576
Densities of integer sets represented by quadratic forms (w/ P.L. Clark, J. Rouse, and K. Thompson)
2024
J. Number Theory 256, 290–328
Review of Excursions in Algebra, Number Theory, and Analysis
2024
Math. Intelligencer 46, 297–299
Distribution mod p of Euler’s totient and the sum of proper divisors (w/ N. Lebowitz-Lockard and A. Singha Roy)
2024
Michigan Math. J. 74, 143–166
Half-factorial real quadratic orders
2024
Arch. Math. (Basel) 122, 491–500
Z[√−5]: halfway to unique factorization
2024
Amer. Math. Monthly 131, 712–717
Maximally elastic quadratic fields
2025
J. Number Theory 267, 80–100
Two variants of a theorem of Schinzel and Wójcik on multiplicative orders
2025
Acta Arith. 218, 337–345
Towards a Schinzel–Wójcik theorem for number fields
2025
European J. Math. 11, no. 2, paper no. 26, 16 pages
Mean values of multiplicative functions and applications to residue-class distribution (w/ A. Singha Roy)
2025
Proc. Edinburgh Math. Soc. 68, 712–730
Counting primes with a given primitive root, uniformly (w/ K. (S.) Fan)
2025
Mathematika 71, paper e70055, 30 pp
Revisiting the Lind–Reichardt counterexample to Hasse’s local-global principle (w/ D.B. Leep and D.B. Shapiro)
2025
Amer. Math. Monthly 132, 839–847
Elementary abelian Sylow subgroups of the multiplicative group (w/ S. Morales and G. Polanco)
2026
J. Number Theory 281, 205–223
Partioning powers into sets of equal sum (w/ E. Treviño)
2026+
Rocky Mountain J. Math. (to appear)
Extremal elasticity of quadratic orders (w/ K. (S.) Fan)
2026+
The ideal theory and arithmetic of rings, monoids, and semigroups (Palermo, 2024). Edited by S.T. Chapman. AMS Contemporary Mathematics series (to appear).
Books
Not always buried deep: A second course in elementary number theory
2009
American Mathematical Society
A conversational introduction to algebraic number theory
2017
American Mathematical Society
Steps into analytic number theory (with A. Singha Roy)
2021
Springer
Unreal analysis: Glimpses of the p-adic realm
2024
Ross Mathematics Foundation
Service Activities
Editorial positions
Editor for the American Mathematical Monthly (2016–present).
Editor for the International Journal of Number Theory (2017–present).
Editor for AMS Student Mathematical Library (2022–present).
Editor for Integers journal (2022–present).
Editor for Frontiers in Combinatorics and Number Theory (2025–present).
Ross Mathematics Foundation
Board member (2018–present). The Ross Mathematics Foundation oversees the Ross Mathematics Program.
Refereeing
Has refereed for Acta Arith., Adv. Math., Algebra Number Theory, Amer. Math. Monthly, Bol. Soc. Mat. Mexicana, Bull. Aust. Math. Soc., Bull. Brazilian Math. Soc., Bull. Korean Math. Soc., Canad. Math. Bull., Canad. J. Math., Exp. Math., Integers, Int. J. Number Theory, Int. Math. Res. Notices, J. Integer Sequences, J. Logical and Algebraic Methods in Programming, J. Number Theory, J. Combinatorics and Number Theory, Math. Ann., Math. Comp., Mathematika, Res. Number Theory, Statist. Probab. Lett., and the Handbook of Finite Fields.
Has refereed grant proposals for the National Security Administration and served on National Science Foundation grant panels in 2015, 2017, 2020, and 2022.
Served on an internal UGA awards committee in 2024.
Special session organizer
Co-organized (with L. Goldmakher, M. Milinovich, and J. Kish) a special session at the 2012 AMS/MAA Joint Meetings titled “New perspectives on multiplicative number theory.” This session followed an NSF-sponsored Mathematics Research Communities workshop, “The pretentious view of analytic number theory.”
For the 2014 Joint Meetings, co-organized (with C. Pomerance) an MAA Invited Paper Session titled “The continuing influence of Paul Erdős in number theory”.
Organized the special session “Elementary methods in analytic number theory” at the Spring 2015 Southeastern AMS Sectional Meeting in Huntsville, Alabama (March 27–29, 2015).
Organized (with R. Lemke Oliver and F. Thorne) a special session for the 2017 AMS/MAA Joint Meetings titled “Analytic number theory and arithmetic” (January 7, 2017).
Member of the conference organizing committee for Integers Conference 2023 and 2025.
Teaching in developing countries
Taught a one-week course in Manila in July 2013 for a summer school on algebraic curves. The summer school was sponsored by CIMPA (International Centre for Pure and Applied Mathematics) and ICTP (the Abdus Salam International Centre for Theoretical Physics), organizations that promote scientific education in the developing world.
In Summer 2017 and Summer 2019, taught minicourses in number theory at the Universidad Autónoma de Santo Domingo (UASD), in the Dominican Republic.
Was a co-PI on two Fondocyt (Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico) research grants for graduate-level research projects with Dominican students, 2020–2022.
Co-PI on a Fondocyt grant for research with Dominican student Samuel Morales and currently coadvising (with Geremias Polanco and Enrique Treviño) Dominican Ph.D. students Andradis Elieser Luna Martinez and Samuel Morales.
Work with junior mathematicians
Served on a Young Mathematicians’ Network panel at the 2016 AMS/MAA Joint Meetings on “Finding a thesis topic and advisor.” Co-panelist with Allison Henrich of Seattle University.
Served as one of the primary contest organizers for the University of Georgia high school math tournament from 2013–2022 and remains involved in contest design and grading supervision.
Was a faculty mentor for the week-long UGA MathCamp in the summers of 2013, 2014, and 2016.
Was one of 11 speakers at the 60th anniversary Ross Program reunion conference in June 2017.
Co-ran the Ross Mathematics Asia Program in Huangshan City, Anhui, China, in Summer 2018 (with Enrique Treviño, Lake Forest College). Taught Advanced Courses at the 2019 Ross Asia Program in Zhenjiang, Jiangsu, China, and the 2020 and 2021 Ross Programs online. Co-taught the number theory lectures in 2022 in Ohio and delivered the number theory lectures in 2023 in Indiana. Taught advanced courses in 2024 and 2025 in Indiana.
Served as one of the “mathematicians in residence” at the Summer 2022 Budapest Semesters in Mathematics program (with Enrique Treviño).
Related site: Ross Mathematics Program website
Mentoring
Postdoctoral mentor
- Lola Thompson (2012–2013)
- Joseph Vandehey (2013–2016)
- Joshua Stucky (2022–2024)
- Kai (Steve) Fan (2025–present)
Thesis supervisor
- Emily Jennings (M.A., 2014)
- Lee Troupe (Ph.D., Spring 2016)
- Noah Lebowitz-Lockard (Ph.D., Spring 2019)
- Kubra Benli (Ph.D., Spring 2020)
- Matthew Just (Ph.D., Summer 2021)
- Komal Agrawal (Ph.D., Spring 2022)
- Patrick Akande (Ph.D., Spring 2024)
- Akash Singha Roy (Ph.D., Summer 2025)
- Paco Adajar (Ph.D., in progress)
- Casia Siegel (Ph.D., in progress)
- Rishika Agrawal (Ph.D., in progress; co-advising with Giorgis Petridis)
Undergraduate research supervisor
- Jackson Douglas Hopper (2015–2017); Jackson received a $1000 CURO research assistantship in Spring 2015 and a $3000 CURO summer fellowship in Summer 2015. Their work on “digitally delicate” primes appeared in the Journal of Number Theory (paper #73 above).
UGA Teaching Experience
| Course | Term |
|---|---|
| MATH 2260: Calculus II for science and engineering | Fall 2012 |
| MATH 3220: Advanced problem solving | Fall 2012 |
| MATH 3100: Sequences and series | Spring 2013 |
| MATH 4400/6400: Elementary number theory | Spring 2013 |
| MATH 3220: Advanced problem solving | Fall 2013 |
| MATH 8440: Advanced topics in elementary number theory | Fall 2013 |
| MATH 3100: Sequences and series | Spring 2014 |
| MATH 3220: Advanced problem solving | Fall 2014 |
| MATH 4150: Complex variables | Fall 2014 |
| MATH 3100H: Sequences and series (Honors) | Spring 2015 |
| MATH 3220: Advanced problem solving | Fall 2015 |
| MATH 4000: Modern algebra and geometry I | Fall 2015s |
| MATH 8850: Introduction to mathematical research (joint w/ P. L. Clark) | Fall 2015 |
| MATH 3100H: Sequences and series (Honors) | Spring 2016 |
| MATH 8400: Algebraic number theory | Spring 2016 |
| MATH 8850: Introduction to mathematical research (joint w/ P. L. Clark) | Spring 2016 |
| MATH 3220: Advanced problem solving | Fall 2016 |
| MATH 4000: Modern algebra and geometry I | Fall 2016 |
| MATH 3100H: Sequences and series (Honors) | Spring 2017 |
| MATH 4400/6400: Elementary number theory | Spring 2017 |
| MATH 3100: Sequences and series | Fall 2017 |
| MATH 3220: Advanced problem solving | Fall 2017 |
| MATH 8400: Algebraic number theory | Fall 2017 |
| MATH 3220: Advanced problem solving | Fall 2017 |
| MATH 8400: Algebraic number theory | Fall 2017 |
| MATH 4000: Modern algebra and geometry I | Spring 2018 |
| MATH 8440: Analytic number theory | Fall 2018 |
| MATH 4000: Modern algebra and geometry I | Fall 2018 |
| MATH 4000: Modern algebra and geometry I | Spring 2019 |
| MATH 4400/6400: Elementary number theory | Spring 2019 |
| MATH 3100: Sequences and series (×2) | Spring 2020 |
| MATH 3200: Introduction to higher mathematics | Spring 2020 |
| MATH 3100: Sequences and series | Fall 2020 |
| MATH 3220: Advanced problem solving | Spring 2021 |
| MATH 8400: Algebraic number theory | Spring 2021 |
| MATH 4400/6400: Elementary Number Theory | Spring 2021 |
| MATH 3220: Advanced problems solving | Fall 2021 |
| MATH 3100: Sequences and series | Fall 2021 |
| MATH 4000: Modern algebra and geometry I | Spring 2022 |
| MATH 4400/6400: Elementary number theory | Spring 2022 |
| MATH 3100: Sequences and series | Fall 2022 |
| MATH 4400: Elementary Number Theory | Spring 2023 |
| MATH 8440: Multiplicative Number Theory | Spring 2023 |
| MATH 3100: Sequences and series | Fall 2023 |
| MATH 8440: Topics in Analytic Number Theory | Fall 2023 |
| MATH 3100: Sequences and series | Spring 2024 |
| MATH 4000: Modern algebra and geometry I | Spring 2024 |
| MATH 3100: Introduction to Mathematical Analysis | Fall 2024 |
| MATH 3200: Introduciton to higher mathematic | Fall 2024 |
| MATH 4000: Modern algebra I | Spring 2025 |
| MATH 3100/3100H: Introduction to Mathematical Analysis | Fall 2025 |
| MATH 4000: Modern Algebra | Spring 2026 |