I am a lecturer in Political Science and Computer Science at Yale University. My office is Rosenkranz 107. You can reach me at email@example.com.
In Fall 2020 I am teaching PLSC 529, Mathematics for Political Science, and CPSC 460/560, Automata Theory and Formal Languages. See Canvas for more information.
“Mahler equations of p-regular series via difference algebra of weighted automata,” in preparation.
“A question for iterated Galois groups in arithmetic dynamics,” (with John Doyle, Dragos Ghioca, Liang-Chung Hsia, and Thomas J. Tucker), Canad. Math. Bull., to appear.
“The Arakelov-Zhang pairing and Julia sets,” (with Matt Larson), submitted
“Finite index theorems for iterated Galois groups of unicritical polynomials,” (with John Doyle, Dragos Ghioca, Liang-Chung Hsia, and Thomas J. Tucker), Trans. Amer. Math. Soc., to appear.
“The cycle structure of unicritical polynomials,” (with Derek Garton), Int. Math. Res. Not. IMRN, to appear.
“Finite index theorems for iterated Galois groups of cubic polynomials, (with Thomas J. Tucker), Math. Ann. 373 (2019), no. 1-2, 37–72.
“ABC Implies a Zsigmondy Principle for Ramification,” (with Thomas J. Tucker), J. Number Theory 182 (2018), 296–310.
“The generalized Nagell-Ljunggren problem: powers with repetitive representations,” (with Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit), Experimental Mathematics, to appear.
“Finite Ramification for Preimage Fields of Postcritically Finite Morphisms,” (with Patrick Ingram, Rafe Jones, Jamie Juul, Alon Levy, Michelle Manes, Simon Rubinstein-Salzedo, and Joseph Silverman), Math Res. Lett. 24 (2017), no. 6, 1633–1647
“Dynamically Distinguishing Polynomials,” (with Derek Garton), Res. Math. Sc 4 (2017), no. 13, 1–17.
“Automatic Sequences and Curves over Finite Fields,” Algebra and Number Theory 11 (2017), no. 3, 685–712.
“The Artin-Mazur Zeta Function of a Dynamically Affine Rational Map in Positive Characteristic,” J. Théor. Nombres Bordeaux, 28 (2016), no. 2, 301–324.
“On the Number of Distinct Functional Graphs of Affine-Linear Transformations over Finite Fields,” (with Eric Bach), Linear Algebra and Appl. 439 (2013), 1312–1320.
“Transcendence of the Artin-Mazur Zeta Function for Polynomial Maps of A^1(F_p),” Acta Arith.156 (2012), no. 3, 293–300.
“A Count of Maximal Small Copies in Multibrot Sets,” (with Rodrigo Pérez), Nonlinearity 18 (2005), no. 5, 1945-1953.