From September 2015 I am Principal Investigator for a two year long European Union funded research project LDMRD "Large Deviations and Measure Rigidity in Dynamics" under the Marie Skłodowska-Curie Actions EF scheme as a part of Horizon 2020 programme. The project is hosted by the University of Bristol, UK. Parts of the work will also be done in Universidad Torcuato Di Tella, Argentina, Pontificia Universidad Católica de Chile, Chile, University of Helsinki, Finland, and The Hebrew University of Jerusalem, Israel.

Goals

The project aims to develop new tools in ergodic theory and dynamical systems, and explore applications to problems related to mathematical physics, geometry and arithmetics. The first general objective is to advance large deviation theory for non-compact dynamical systems. We plan to deduce new subexponential large deviation bounds for Gibbs measures on the countable Markov shift and explore how these results are linked to Manneville-Pomeau dynamics describing intermittence in the theory of turbulent flows, dynamical properties of the Gauss map, which is deeply connected to Diophantine approximation, and homogeneous dynamics such as the Teichmüller flow on translation surfaces. The second general objective is to investigate Host-type measure rigidity theory for toral automorphisms and homogeneous dynamics. This topic relates to currently ongoing research on measure classification theorems, which have been influential in several applications such Diophantine approximation and quantum ergodicity. The main tools used in these works are additive combinatorics, thermodynamical formalism, and the spectral/ergodic theory of the scenery flow.

Research output

  1. Pointwise perturbations of countable Markov maps, with T. Jordan and S. Munday
    arXiv:1601.06591, Preprint (2016)
  2. Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces, with Etienne Le Masson
    Duke Math. J. (2017), to appear
  3. Large deviations for the countable Markov shift, with A. Ferguson and T. Jordan, preprint
  4. Large deviations for the Teichmüller flow, preprint

Outreach