Existence of physical measures for smooth surface diffeomorphisms

Marcelo Viana has conjectured that a smooth diffeomorphism admits a physical measure if the Lyapunov exponents of its orbits in a full volume set do not vanish. I will explain how a technique controlling the continuity of Lyapunov exponents allows to prove this conjecture in the case of smooth surface diffeomorphisms. This is a joint work with Jérôme Buzzi and Omri Sarig.