## Andrew Bridy

Yale University Department of Computer Science and Department of Political Science

**Address:** PO Box 208301, Yale University, New Haven, CT 06520-8301

**Office:** Rosenkranz 107

**E-mail:** andrew.bridy [AT] yale.edu

### Teaching

In Fall 2019 I am teaching PLSC 529 and CPSC 460/560.

### Travel

University of Calgary, Aug. 19-23

UConn, Sept. 11

Utrecht University, Oct. 14-18

### Research

My research interests are mainly in number theory and algebraic geometry, particularly in arithmetic dynamics. I study arithmetic and algebraic properties of dynamical systems, such as the arboreal Galois representations attached to preimage fields of rational maps and the cycle structure of polynomials in finite fields. I am also very interested in the connections between automata theory and number theory.

### CV

### Papers

"Iterated monodromy groups of rational functions and periodic points over finite fields" (with Rafe Jones, Greg Kelsey, and Russell Lodge), in preparation

"Mahler equations of p-regular series via difference algebra of weighted automata," in preparation.

"Toward the inverse Galois problem for polynomial systems," (with Frank Sottile), in preparation.

"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), submitted.

"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. Sci.* 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.

### Talks