Alejandro Kocsard (Universidade Federal Fluminense) 
The Burnside problem for groups of diffeomorphisms

Abstract: An abstract group is called periodic when every element of the group has finite order. In 1901 W. Burnside proposed the following problem: 
Is a finitely generated periodic group necessarily finite?

The first (counter-)examples to Burnside's problem only appeared in 1964, in a work of Golod and Shafarevich.

Following the philosophy of the so called Zimmer's program, it is natural to consider whether these infinite finitely generated periodic groups are "geometric", i.e. if they can faithfully act on manifolds.

In this talk we shall discuss some recent results about the non-geometric nature of them and how dynamical and probabilistic tools are used to deal with this kind of problems.