In Measures of maximal entropy for surface diffeomorphisms appeared in the Annals, Buzzi, Crovisier and Sarig proved that (from the Abstract) "$C^\infty$-surface diffeomorphisms with positive topological entropy have finitely many ergodic measures of maximal entropy in general, and exactly one in the topologically transitive case".

Looks like a major result to me, although I'm biased towards dynamical systems.

In Measures of maximal entropy for surface diffeomorphisms appeared in the Annals, Buzzi, Crovisier and Sarig proved that (from the Abstract) "$C^\infty$-surface diffeomorphisms with positive topological entropy have finitely many ergodic measures of maximal entropy in general, and exactly one in the topologically transitive case".

It is a huge result in smooth dynamics, and it looks like a major result in general to me, although I'm biased towards dynamical systems.