Davit Karagulyan: Hausdorff dimension of a class of three-interval exchange maps'

I will talk about the Möbius disjointness conjecture of P. Sarnak and discuss a result of Bourgain, which establishes the conjecture for a class of Three-interval exchange maps. We will present a result where we estimate the measure of the set of parameters which satisfy the Diophantine condition of Bourgain. As a consequence we show that it has positive, but not full Hausdorff dimension.