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Faculty

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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)

Website
Curriculum Vitae


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 (2016), no. 7, 2885–2899. (journal |arXiv)
  • Computing algebraic numbers of bounded height (with David KrummMath. 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)

Preprints

  • Preperiodic portraits for unicritical polynomials over a rational function field Submitted. (arXiv)
  • Preperiodic points for quadratic polynomials with small cycles over quadratic fields Submitted. (arXiv)