  We introduce the notion of nonuniform center bunching for partially
hyperbolic diffeomorphims, and extend previous results by Burns--Wilkinson and
Avila--Santamaria--Viana. Combining this new technique with other
constructions, we prove that $C^1$-generic partially hyperbolic
symplectomorphisms are ergodic. We also construct new examples of stably
ergodic partially hyperbolic diffeomorphisms.
