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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

Course: Introduction to ergodic theory