My primary research interests are in number theory, dynamical systems, and group theory. Links to my papers may be found below.
Iterates of post-critically finite polynomials of the form x^d+c, submitted for publication, 2025.
(with Robert L. Benedetto) The non-unit conjecture for Misiurewicz parameters, submitted for publication, 2025.
A note on the factorization of iterated quadratics over finite fields, to appear in Journal de Théorie des Nombres de Bordeaux, 2025.
(with Giacomo Micheli) Square patterns in dynamical orbits, Journal of Number Theory, Volume 272 (2025), Pages 129-146
(with Robert L. Benedetto) Misiurewicz polynomials and dynamical units, Part II, Research in Number Theory , Vol.10, No. 58 (2024).
A local-global conjugacy question arising from arithmetic dynamics , Groups, Geometry, and Dynamics, Volume 18 (2024), no. 2, pp. 635-648.
(with Robert L. Benedetto) Misiurewicz polynomials and dynamical units, Part I, International Journal of Number Theory, Vol. 19, No. 6, pp. 1249-1267 (2023).
A note on Misiurewicz polynomials , Journal de Théorie des Nombres de Bordeaux, Volume 32 (2020), No. 2, p. 373-385.
On the orbit of a post-critically finite polynomial of the form x^d+c, Functiones et Approximatio Commentarii Mathematici, Volume 62, Number 1 (2020), 95-104.
Markov Processes and Some PCF Quadratic Polynomials, Research in Number Theory (2019) 5:29.
Irreducibility of iterates of post-critically finite quadratic polynomials over Q, Rocky Mountain Journal of Mathematics, Volume 49, Number 7 (2019), 2155-2174.
(with S. Xia and N. Boston) A refined conjecture for factorizations of iterates of quadratic polynomials over finite fields, Experimental Mathematics , Vol 24 (3), 304–311, 2015.