Logo

The Parallels between Topological Dynamics and Ergodic Theory 99

4046e6cf870c380272e12e95bd8d18d37a7f2656

Speaker

Xiangdong Ye, University of Science and Technology of China, China

Time

2020.06.12 10:00-11:00

Venue

Online—ZOOM APP

ZOOM Info

ZOOM Link

Conference ID: 684-150-51078

PIN Code:189308

Abstract

Topological dynamics and ergodic theory are twin branches in the field of dynamical systems, which have deep applications to combinatorial number theory.

I will explain the connection among them by examples. The first example we give is the structure theorems, focused on works by Furstenberg, Ellis-Glasner-Shapiro, Host-Kra, Host-Kra-Maass and Shao-Ye. The second example we take is the study around the multiple ergodic averages, based on works by Furstenberg, Host-Kra, Bourgain, Huang-Shao-Ye and on a recent work by Glasner-Huang -Shao-Weiss-Ye.

Bio

叶向东,中国科学技术大学教授,国家杰出青年科学基金获得者,教育部长江学者特聘教授。曾任中国数学会副理事长,现任安徽省数学会理事长。获第十四届陈省身数学奖;2018年国家自然科学二等奖(第一完成人)。2019年当选中国科学院院士。

他长期从事基础数学中拓扑动力系统、遍历理论及其应用的研究。他与合作者对动力系统的结构及逐点多重遍历定理、熵理论、复杂性层次等进行了深入系统的研究,经过多年不懈的努力,该研究得到极小系统更精细的结构定理;证明了遍历distal系统的逐点多重遍历定理;得到正熵系统新的刻画;给出Furstenberg不交性问题的一个充分必要条件;证明了 Devaney 混沌蕴含 Li-Yorke混沌等。

Sponsors