Continued Fractions, Interval Exchanges and Applications to Geometry

Partially supported by UMI no. 3483

11 June 2013 - 14 June 2013

Aims

The workshop will focus on the interplay between dynamical systems and arithmetic, and in particular on the study of arithmetic algorithms of significance in dynamics and geometry. Since the discovery of a relation between the continued fraction algorithm and the geodesic flow on the modular surface, a vast field of research has developed whose main goal is to understand the dynamics of geometric flows in terms of discrete arithmetic algorithms. Of particular importance in this picture are interval exchange transformations, which code the Teichmuller geodesic flow. In the workshop, we will discuss recent developments in the metric theory of continued fractions and their various generalizations (one- and multidimensional), as well as interval exchange maps and their applications to Teichmuller theory.

Some funds are available to offer financial support to a number of selected young researchers and students for their participation in the workshop. Please see "Financial support" for more details.

Please also see "Planned activities" for additional information about the programme.