(On Sabbatical through September 2024)

Before Bard, I received my PhD in mathematics from the University of Massachusetts in 2005 under the direction of Siman Wong. I graduated from Bates College in 1999 with a double-major in mathematics and physics. I am originally from Yonkers, NY and went to high school at ECFS. In my non-mathematical life I race bikes, go hiking, and do a lot of yoga.

Contact: cullinan at bard dot edu; Albee 300

32. The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, II (w/ S. Dobson, L. Frey, A. Hamakiotes, R. Hernandez, N. Kaplan, J. Mello, G. Scullard). Submitted 2024.

31. On the modular Plesken Lie algebra

Submitted, 2024.

30. On the discriminant of the truncated logarithmic polynomials (w/ R. Gajek-Leonard)

Submitted, 2023.

29. On the Irreducibility of the Krawtchouck Polynomials

Submitted, 2023.

28. Towards a Universal Gibbs Constant (w/ Antu Santanu)

Submitted, 2023.

27. Realizations of unisingular representations by hyperelliptic Jacobians.

Communications in Algebra

26. The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, I (w/ N. Kaplan).

Research in Number Theory

25. On the arithmetic of Pade approximants to the exponential function (w/ V. Scheel).

Journal of the Ramanujan Mathematical Society

24. On a probabilistic local-global principal for torsion on elliptic curves (w/ J. Voight, M. Kenney).

Journal de Théorie des Nombres de Bordeaux

23. Divisibility of torsion subgroups of abelian surfaces over number fields (w/ J. Yelton).

Canadian Journal of Matheamatics

22. Unisingular representations in arithmetic and Lie theory (w/ A. Zalesski).

European Journal of Mathematics (2021)

21. A remark on the group structure of 2-isogenous elliptic curves in towers of finite fields.

New York Journal of Mathematics

20. Fixed-Point Subgroups of GL(3,q).

Journal of Group Theory

19. On the Jacobians of curves defined by the Generalized Laguerre Polynomials.

Experimental Mathematics

18. Voting with partially ordered preferences (w/ S. Hsiao).

Mathematics for Social Justice: Resources for the College Classroom

AMS/MAA Classroom Resource Materials

17. A remark on the group structure of elliptic curves in towers of finite fields.

New York Journal of Mathematics.

16. Algebraic properties of Kaneko-Zagier lifts of supersingular polynomials (w/ F. Hajir).

Proceedings of the American Mathematical Society 145 (2017), no. 6, 2291-2304.

15. Real preimages of duplication on elliptic curves.

Missouri Journal of Mathematical Sciences 29 (2017), no. 1, 19-26.

14. On the Newton polygons of Kaneko-Zagier lifts of supersingular polynomials (w/ R. Gajek-Leonard).

Research in Number Theory 2 (2016), Art. 34

13. On the solution to a generalized Fermat equation: arithmetic and combinatorics (w/ A. Barghi).

Journal of Combinatorics and Number Theory 7 (2015), no. 3, 157-169.

12. Arithmetic properties of generalized Rikuna polynomials (w/ Z. Chonoles et al).

Publications Mathematiques de Besancon: Algebre et Theorie des Nombres, 2014/1, 19-33.

11. On the ranks of Jacobians of curves defined by Jacobi polynomials (w/ A. Etropolski and E. Sell).

Rocky Mountain Journal of Mathematics 44 (2014), no. 1, 23-33.

10. On the Galois groups of Legendre polynomials (w/ F. Hajir).

Indagationes Mathematicae (N.S.) 25 (2014), no. 3, 534-552.

9. A Borda Count procedure for partially ordered ballots (w/ S. Hsiao and D. Polett).

Social Choice Welfare 42 (2014), no. 4, 913-926.

8. Specializations of generalized Rikuna polynomials (w/ C. Cass, A. Rasmussen, and D. Trifunovski).

International Journal of Number Theory 10 (2014), no. 3, 585-600.

7. Primes of prescribed congruence class in short intervals (w/ F. Hajir).

Integers 12 (2012) #A56.

6. Symplectic stabilizers with applications to abelian varieties.

International Journal of Number Theory 8 (2012), no. 2, 321-334.

5. Ramification in iterated towers for rational functions (w/ F. Hajir).

Manuscripta Mathematica 137 (2012), no. 3-4, 273-286.

4. Points of small order on three-dimensional abelian varieties; With an appendix by Yuri Zarhin.

Journal of Algebra 324 (2010), no. 3, 565-577.

3. Algebraic properties of a family of Jacobi polynomials (w/ F. Hajir and E. Sell).

Journal de Theorie des Nombres de Bordeaux 21 (2009), no. 1, 97-108.

2. A computational approach to the 2-torsion structure of an abelian threefold.

Mathematics of Computation 78 (2009), no. 267, 1825-1836.

1. Local-global properties of torsion points on three-dimensional abelian varieties.

Journal of Algebra 311 (2007), no. 2, 736-774

My research is primarily in arithmetic geometry and representation theory. The online databases that I use most in my research are the LMFDB, the Atlas of finite groups, and Tim Dokchitser's GroupNames project.

Here are a few expository things I've written up for students: Steinberg Representation, Discriminant Lemma.

I enjoy writing for Math Reviews. To read any of the ~100 reviews I've written, or to access the database in general, you'll need a site license.

Here are some of my favorite mathematical videos:

Serre's Minerva lectures 1, 2, and 3 and Serre on Writing Mathematics Badly

Katz's IHES colloquium

The FLT Conference.