email: tsharland at uri dot edu
Office: 202F, Lippitt Hall
I am currently an Assistant Professor in the Department of Mathematics at the University of Rhode Island.
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.
I am also investigating combinatorial invariants of bicritical rational maps, and studying slices of the parameter space of cubic rational maps.
- 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).
- 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 (2013).
- Matings of cubic polynomials with a fixed critical point, in progress. Here is a short note that makes up part of this study, showing that all irreducible obstructions for cubic branched coverings with two fixed critical points are Levy cycles.
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.
In Spring 2018, I am teaching
My office hours are:
or by appointment.
- Monday 10.30-11.30
- Tuesday 11-12
- Wednesday 9.30-10.30
Teaching from previous semesters at URI
Previous Teaching at Stony Brook
Guardian crossword page
BBC iPlayer radio