** 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.**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**, submitted. 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.

- On local connectivity of $\mathcal{S}_2$ in the parameter space of cubic polynomials (with A. Bonifant and C. Estabrooks)
- Identifications in escape regions of the parameter space of cubic polynomials (with A. Bonifant and C. Estabrooks)
- Thurston obstructions for cubic branched coverings with two fixed critical points.

My thesis which I completed at the Mathematics Institute at the University of Warwick. My advisor was Adam Epstein.

- 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 Fall 2018, I am teaching

My office hours are:- Monday 11-12
- Tuesday 3-4
- Thursday 2-3

Previous Teaching at Stony Brook

- 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.

Guardian crossword page

BBC iPlayer radio

Contact me