Date:	Fri, September 24, 2010
Time:	14:15
Place:	Research I Seminar Room

Abstract: A well-known conjecture, stated in 70s by many authors, says, that a smooth action on the circle of a finitely generated group on the circle, that does not have any nontrivial closed invariant subsets (i.e. is minimal), does not have any nontrivial measurable invariant subsets (i.e. is Lebesgue-ergodic).

This conjecture was proved in the case of one diffeomorphism be Katok and Hermann, and by Sullivan for groups satisfying the expansion property.

We will discuss the ways of attacking this conjecture for non- commutative groups without the expansion property, the structure of such groups, and a recent result showing the conjecture for free groups of analytic diffeomorphisms.

(Joint work with B. Deroin, D. Filimonov, A. Navas.)