Manchester Geometry Seminar 2011/2012

Wednesday 26 October 2011. Joint Seminar: Dynamical Systems, Geometry, and Topology.
The Frank Adams Room FA1 (Room 1.212), the Alan Turing Building. 3.30pm

Ziggurats and Rotation Numbers

Danny Calegary (University of Cambridge)

I will discuss new rigidity and rationality phenomena (related to the phenomenon of Arnold tongues) in the theory of nonabelian group actions on the circle. I will introduce tools that can translate questions about the existence of actions with prescribed dynamics, into finite combinatorial questions that can be answered effectively. There are connections with the theory of diophantine approximation, and with the bounded cohomology of free groups. A special case of this theory gives a very short new proof of Naimi's theorem (i.e. the conjecture of Jankins-Neumann) which was the last step in the classification of taut foliations of Seifert fibered spaces. This is joint work with Alden Walker.