# Faculty

## John Doyle

*Visiting Assistant Professor of Mathematics*

PhD, University of Georgia, 2014

1019 Hylan Hall

(585) 275-4419

jdoyle21@ur.rochester.edu

Office Hours: Th 10 – 11:30 and 12:30 – 2 (Spring 2016)

### Research Overview

My main research interests lie in the areas of arithmetic dynamics and algebraic number theory. Generally speaking, arithmetic dynamics is the study of the dynamics of rational maps defined over fields of arithmetic interest, like number fields and p-adic fields. Much of my work has involved studying properties of certain algebraic curves known as dynamical modular curves, which parametrize maps together with points exhibiting certain behaviors under iteration by those maps. I'm also interested in rational dynamics on the Berkovich projective line.

### Courses Offered (subject to change)

- MTH 142 Calculus II
- MTH 200W Transition to Higher Mathematics

### Selected Publications

#### Publications

**Configuration of the crucial set for a quadratic rational map**(with Kenneth Jacobs and Robert Rumely).*Res. Number Theory*, to appear. (arXiv)**Preperiodic portraits for unicritical polynomials***Proc. Amer. Math. Soc.***144****Computing algebraic numbers of bounded height**(with David Krumm)*Math. Comp.***84**(2015), no. 296, 2867–2891. (journal | arXiv)**Preperiodic points for quadratic polynomials over quadratic fields**(with Xander Faber and David Krumm).*New York J. Math.***20**(2014), 507–605. (journal | arXiv)**Apollonian circle packings of the half-plane**(with Michael Ching)*J. Comb.***3**(2012), no. 1, 1–48. (journal | arXiv)