I work in ergodic theory and dynamical systems. I am interested in the stochastic behavior of deterministic dynamical systems, especially those which are non-uniformly hyperbolic, or which act on non-compact spaces, or which possess natural infinite invariant measures.
Here are some of the topics I have worked on in the past:
1. Thermodynamic formalism for maps with infinite Markov partitions
2. Sub-exponential decay of correlations
3. Horocycle flows on hyperbolic surfaces of infinite genus
4. Markov partitions for non-uniformly hyperbolic dynamical systems
5. Skew products over irrational rotations
6. Temporal distributional limit theorems