# Meeting Details

Title: Conservative diffeomorphisms from a C^1 generic perspective. ATTENTION : THIS SEMINAR WILL BEGIN AT 4:40PM Center for Dynamics and Geometry Seminars Amie Wilkinson, University of Chicago Let $M$ be a closed manifold endowed with a volume form. I will discuss two related results about the volume-preserving diffeomophisms of $M$, which are recent work with Artur Avila and Sylvain Crovisier. Theorem A: Consider the set of all $C^1$, volume-preserving diffeomorphisms of $M$ endowed with the $C^1$ topology. Then there is a residual subset $R$ so that for every $f\in R$, if $f$ has positive metric entropy, then $f$ is ergodic and nonuniformly Anosov. Theorem B: Among the set of all $C^r$, partially hyperbolic diffeomorphisms of $M$, with $r\geq 2$, stable ergodicity is $C^1$ dense. ATTENTION : THIS SEMINAR WILL BEGIN AT 4:40PM