Thomas Barthelmé
Associate Professor
| Office: | Jeffery Hall, Rm. 504 |
|---|---|
| Phone: | (613) 533-6640 |
| Email: | thomas.barthelme@queensu.ca |
| Website: | |
| Research: | Hyperbolic dynamical systems, finsler & riemannian geometry, flows in 3-manifold, ergodic geometry |
Degrees & Accolades:
Ph.D. (Université de Strasbourg)
Master (Université de Strasbourg)
License (Université de Strasbourg)
Research Profile:
My research interests lie in between geometry, topology and dynamical systems with a focus on problems mixing this three domains, either in the origin of the questions, or in the proofs. My main two axes of research are concerned with dynamical systems in low dimensional manifolds on one side and the geometry and dynamics of Finsler metrics on the other.
The unifying theme that underlies my research is a connection between geometry, topology and dynamics: I use geometrical or topological tools to study dynamical systems and study dynamical flows coming from a geometrical setting.
I am looking to hire graduate students who are interested in working in geometry or dynamics.
Research Areas:
Problem 1: Writing an algorithm that produces a list of 3manifolds supporting Anosov flows. Anosov flows are a fundamental and central class of examples in smooth dynamical systems, but we still don’t know much about which 3manifolds can support them. Recent advances in the field opens the possibility of exploring algorithmically these manifolds.
Problem 2: Symmetries of (pseudo)-Anosov flows and partially hyperbolic diffeomorphisms. Conjecturally all partially hyperbolic diffeomorphisms in dimension 3 are related (semiconjugated) to some symmetries of Anosov flows. This naturally leads to do questions: can one describe all the symmetries of a (pseudo)-Anosov flow, and, given such a symmetry, can one build a related partially hyperbolic diffeomorphism?
Problem 3: Centralizers of partially hyperbolic diffeomorphisms. A classical question in dynamics is to understand the centralizer of a system, i.e., all the diffeomorphisms that commute with a given dynamical system. In the case of certain partially hyperbolic diffeomorphisms, Damjanovic, Wilkinson, and Xu proved a beautiful dichotomy: The centralizer is either (virtually) trivial, or (virtually) isomorphic to Z, in which case the diffeomorphism is very specific. The goal of this problem is to generalize this result to a much wider class of partially hyperbolic diffeomorphisms in dimension 3.