# 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)

`dannyc@its.caltech.edu`

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.