Tom Sharland

Contact Information

email: tsharland at uri dot edu
Office: 202F, Lippitt Hall
Phone: (401)-874-2314

I am currently an Assistant Professor in the Department of Mathematics at the University of Rhode Island. Starting Fall (autumn) 2018, I am also the Graduate Director of Mathematics at URI.
I was previously a Milnor lecturer at Stony Brook University.

My research is mainly focused on one-dimensional holomorphic dynamics, in particular Thurston equivalence of rational maps, matings of polynomials and the study of spaces of rational maps. I am also interested in related subjects, such as Teichmüller theory, Riemann surface theory and topological dynamics.

Araceli Bonifant and I have set up a Dynamics seminar at URI. Here is the web page for the dynamics group.

Research

Articles

A classification of bicritical rational maps with a pair of period two superattracting cycles (with Adam Epstein), Annales de la Faculté des Sciences de Toulouse, volume XXI, number 5, pp. 907-934 (2012).
Thurston equivalence of rational maps with cluster cycles, Ergodic Theory and Dynamical Systems, volume 33, issue 04, pp. 1178-1198 (2013).
Constructing rational maps with cluster cycles using the mating operation, Journal of the London Mathematical Society, volume 87, issue 1, pp. 87-110 (2013).
Matings of cubic polynomials with a fixed critical point, Part I: Thurston Obstructions, Conformal Geometry and Dynamics, Volume 23, pp205-220 (2019).
Fractal Matings, Math. Horizons, Volume 29, pp20-23 (2022).
Relations between escape regions in the parameter space of cubic polynomials (with A. Bonifant and C. Estabrooks), Arnold Math. Journal, to appear. Published online July 2022.
Matings of cubic polynomials with a fixed critical point, Part II: (alpha)-symmetry of limbs. Journal of Difference Equations and Applications Published online March 2023.
Bicritical rational maps with a common iterate (with S. Koch and K. Lindsey). International Mathematics Research Notices. Published online March 2023
On the deck groups of iterates of bicritical rational maps (with S. Koch and K. Lindsey). Submitted.

I am also investigating combinatorial invariants of (bicritical) rational maps, and studying slices of the parameter space of cubic rational maps.
My thesis which I completed at the Mathematics Institute at the University of Warwick. My advisor was Adam Epstein.

Posters, talks etc.

My poster presented at ICERM during the conference on Complex and p-adic dynamics.
My talk I gave at the Harvard informal dynamics seminar on 4th April 2012.
My talk I gave at the Stony Brook Dynamical Systems Seminar on the 14th September 2012.
My talk I gave at the Iberoamerican conference at the CUNY Graduate Center, 21st May 2014.

Teaching

In Spring 2023, I am teaching MTH 316: Algebra and MTH 243: Calculus in several variables. My office hours are all in Lippitt 202F at the following times:

Monday 9.30-10.30
Wednesday 11-12.30
Thursday 2-3

Previous Teaching

Teaching from previous semesters at URI

Previous Teaching at Stony Brook

Mathematical Links

The Dynamical Systems group at URI.
Link to my articles on the arxiv.
ICERM, where I was a Visiting Researcher during the Spring semester 2012.
Arnaud Chéritat has some beautiful videos of matings. My particular favo(u)rite is ReesSharedExample, which shows a shared mating.
Wolf Jung has written a nice program, Mandel, for looking at Julia sets and parameter spaces.
Dynamics Explorer is a program by Suzanne and Bryan Boyd which draws pictures from complex dynamics.
My wife Ayşe Altıntaş' papers on arxiv.

Miscellany

Kidderminster Harriers
Guardian crossword page
BBC iPlayer radio

Contact me