Entropy of semiclassical measures in dimension 2
  We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of Anosov type. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound 
Gabriel Riviere (CMLS-EcolePolytechnique)