Andrew Bridy
Postdoctoral Associate, Yale University Department of Mathematics
Address: 10 Hillhouse Ave, New Haven, CT 06511
Office: LOM 218
E-mail: andrew.bridy [AT] yale.edu
Teaching
In Fall 2018 I am teaching Math 115. See the Yale Canvas site for more information.
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
"Iterated monodromy groups of rational functions and periodic points over finite fields" (with Rafe Jones, Greg Kelsey, and Russell Lodge), in preparation
"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.
"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., to appear.
"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