## Andrew Bridy

Instructional Assistant Professor of Mathematics

**Address:** Department of Mathematics, Texas A&M University

Mailstop 3368

College Station, TX 77843-3368

**Office:** Blocker 641A

**Phone:** 979-845-6028 to reach TAMU Math Department (no office phone)

**E-mail:** andrewbridy [AT] tamu.edu

I will be joining the Yale University Department of Mathematics as a Postdoctoral Associate in Fall 2018.
### Travel

### 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

"Weighted automata and minimal Mahler equations of p-regular series," in preparation.

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

"The cycle structure of unicritical polynomials," (with Derek Garton), submitted.

"Finite index theorems for iterated Galois groups of cubic polynomials," (with Thomas Tucker), *Math. Ann.*, to appear.

"*ABC* Implies a Zsigmondy Principle for Ramification," (with Thomas 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.