John Cullinan

Associate Professor of Mathematics

Bard College

about                 research                 teaching                 miscellaneous

My main mathematical interests are in arithmetic geometry, representations of finite groups, and the arithmetic of orthogonal polynomials. I also have side interests in the mathematics of voting. My publications, separated roughly by research topic, are as follows (with chronological numbering):

Local-Global Principles for Abelian Varieties and Galois Representations

21. On a probabilistic local-global principal for torsion on elliptic curves (w/ J. Voight).
In Preparation.

19. Fixed-Point Subgroups of GL(3,q).
Submitted, 2018.

6. Symplectic stabilizers with applications to abelian varieties.
International Journal of Number Theory 8 (2012), no. 2, 321-334.

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.

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

Arithmetic of Orthogonal Polynomials

18. On the Jacobians of curves defined by the Generalized Laguerre Polynomials.
To appear in Experimental Mathematics.

17. 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. On the Newton polygons of Kaneko-Zagier lifts of supersingular polynomials (w/ R. Gajek-Leonard).
Research in Number Theory 2 (2016), Art. 34

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.

7. Primes of prescribed congruence class in short intervals (w/ F. Hajir).
Integers 12 (2012) #A56.

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.

Miscellaneous Elliptic Curve

20. The group structure of l-isogenous elliptic curves in towers of finite fields.
Submitted, 2018.

16. Real preimages of duplication on elliptic curves.
Missouri Journal of Mathematical Sciences 29 (2017), no. 1, 19-26.

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.

Galois Theory of Towers

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.

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.

5. Ramification in iterated towers for rational functions (w/ F. Hajir).
Manuscripta Mathematica 137 (2012), no. 3-4, 273-286.

Voting Theory

14. Voting with partially ordered preferences (w/ S. Hsiao).
To appear in Mathematics and Social Justice: Perspectives and Resources for the College Classroom, MAA Edited Volume.

9. A Borda Count procedure for partially ordered ballots (w/ S. Hsiao and D. Polett).
Social Choice Welfare 42 (2014), no. 4, 913-926.