学术报告 课程名称：Interval Exchange Maps and Translation Surfaces
主讲 人：Dong Han Kim教授（韩国东国大学）
第一讲: Translation surfaces, the geodesic flow and induction algorithms.
12月21日（周一）下午 14:30-18:30 地点：4号楼4141室
第二讲：Diophantine conditions of translation surfaces
12月22日（周二）下午14:30-18:30 地点：4号楼4141室
第三讲：Diophantine approximation and Sturmian coloring on the tree
12月25日（周五）下午14:30-18:30 地点：4号楼4141室
第四讲：Repetition complexity function and irrationality exponents
12月26日（周六）下午14:30-18:30 地点：4号楼4318室
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数学学院
2015年12月17日
课程简介：
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.
主讲人简介：
Dong Han Kim教授是国际动力系统与遍历理论领域的专家，在该领域权威期刊上发表高质量论文20余篇，在动力系统的常返性、丢番图逼近、区间交换映射、无理旋转的收缩靶问题等方面做出不少深刻结果，这些结果被广泛关注和引用，曾获得韩国高等科学院颁发的KIAS学术奖、韩国Suwon大学颁发的资深服务等。他学术非常活跃，不仅是Ergodic Theory and Dynamical Systems, Journal of Modern Dynamics, Nonlinearity, IEEE Transactions on Information Theory等国际著名数学杂志的审稿人，而且是杂志Journal of the Korean Society of Mathematical Education,Series B - Pure and Applied Mathematics的副编辑。并与多个国家的研究机构有着密切联系，多次应邀在国际学术会议上做报告并多次组织国际学术会议。