Michele Triestino

Title: Cantor dynamics and simple left-orderable groups

Abstract: I will present a construction of simple groups of homeomorphisms of the real line. Given a homeomorphism of a Cantor set sigma: X --> X, consider the suspension Y=X x [0,1]/ (x,1)~(sigma(x),0), and look at the group H_0(Y) of homeomorphisms of Y, isotopic to the identity. If sigma is minimal, then H_0(Y) is simple [Aliste-Prieto - Petite], and I will describe countable subgroups T(Y) which are also simple. These are reminiscent of the classical Thompson groups, and feature several nice properties. For instance, when sigma is a minimal subshift, T(Y) is finitely generated. Joint work with Nicolás Matte Bon.

Thomas Koberda

Title: Regularity of Denjoy counterexamples

Abstract: I will survey some results about the possible regularity properties of exceptional diffeomorphisms of the circle. I will then discuss a recent result which organizes many possible moduli of continuity for the first derivative of an exceptional diffeomorphism, and briefly describe some open questions. This talk will represent joint work with Sang-hyun Kim.

Ken'ichi Ohshika

Title: Thurston’s bounded image theorem

Abstract: Thurston’s bounded image theorem constitutes an important step in the proof of his uniformisation theorem for Haken manifolds. The proof of the original strong version of the theorem has been unknown. In all books and expository papers on the uniformisation theorem, only a weaker version of the theorem, which is sufficient for the uniformisation theorem, was proved and used. The original strong form has its own interest from the viewpoint of Kleinian group theory, however. In this talk, I shall give its proof based on techniques involving the recent theory of model manifolds. This is joint work with Cyril Lecuire.

Plinio Murillo

Title: On length of closed geodesics of arithmetic manifolds

Abstract: The purpose of this talk is to illustrate how the arithmetic interact with the geometry and the topology of an arithmetic manifold (more generally, orbifolds). We will do that by discussing some ideas and results concerning lengths of closed geodesics, and relations with other geometric invariants of such spaces.