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. 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.
I am also investigating combinatorial invariants of (bicritical) rational maps, and studying slices of the parameter space of cubic rational maps.
- 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.
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 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
Teaching from previous semesters at URI
Previous Teaching at Stony Brook
Guardian crossword page
BBC iPlayer radio