Our work (with Sylvain Crovisier and Omri Sarig) on the continuity property of Lyapunov exponents of surface diffeomorphisms has now been published online at Inventiones: along sequences of ergodic probability measures that converge weak-* and in entropy to a limiting measure, the exponents also converge.
This has nice consequences for Sinai-Ruelle-Bowen measures (see especially this latter work). It will lead to stronger ergodic properties for the measures of maximal entropy through a new notion of Strongly Positive Recurrent diffeomorphisms (work in progress, also with S. Crovisier and O. Sarig).