March 8, 9, 10, 11 (M, T, W, Th), 10 pm Korea (= 8 am EST)
Sergio Fenley (IAS/Florida State University)
Partial hyperbolic dynamics in dimension 3.
This will be a 4 part minicourse. We will first cover some generalities on PH (partially hyperbolic diffeomorphisms). We then restrict to dimension 3 for the ambient manifold, and discuss Pujals' conjecture, and branching foliations, which in some sense are the main technical tool to analyze certain questions about PH in dimension 3. Then we will discuss PH homotopic to the identity. This is very involved and we obtain an enormous amount of structure for such in hyperbolic manifolds and in Seifert manifolds. Any homeomorphism in a closed hyperbolic 3-manifold has a finite power homotopic to the identity. We then study more PH in hyperbolic 3-manifolds and prove that if there is a PH in such a manifold, then there is also an Anosov flow in the manifold. If there is additional time, one possible topic to cover is collapsed Anosov flows.
March 24 (W) 4 pm
Anthony Genevois (CNRS)