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