Course：Interval Exchange Maps and Translation Surfaces

Speaker：Prof.Dong Han Kim（Dongguk University）

The first lecture: Translation surfaces, the geodesic flow and induction algorithms.

14:30-18:30 P.M. Dec.21, 2015 Room 4141, Building No.4, Wushan Campus

The second lecture: Diophantine conditions of translation surfaces

14:30-18:30 P.M. Dec.22, 2015 Room 4141, Building No.4, Wushan Campus

The third lecture: Diophantine approximation and Sturmian coloring on the tree

14:30-18:30 P.M. Dec.25, 2015 Room 4141, Building No.4, Wushan Campus

The forth lecture: Repetition complexity function and irrationality exponents

14:30-18:30 P.M. Dec.26, 2015 Room 4318, Building No.4, Wushan Campus

Course Introduction

The interval exchange map is a generalization of the irrational rotation. It has very interesting dynamical properties and deeply related with number theory and geometry.The dynamics of irrational rotation is determined by its rotation angle and the continued fraction algorithm is the main tool to deal with the rotation angle.The continued fraction algorithm is generalized by Rauzy, Veech and Zorich to the interval exchange maps.This induction algorithm is strongly related to Teichmuller flow of the moduli space of abelian differentials as the usual continued fraction algorithm can be considered as the geodesic flow of the modular space.In this lecture series, we will study the continued fracttion algorithm and suspension of the interval exchage map and follow the big theorems like almost everywhere unique ergodicity of the interval exchange map.