学术报告

走向现代数学-系列学术报告(No.446)(连政星 助理教授)

题目:Maximal pronilfactors and a topological Wiener-Wintner Theorem

报 告 人:连政星 助理教授(厦门大学)

报告时间:2021年8月23日16:30

报告地点:腾讯会议在线报告,会议ID:762 569 042

摘要:For strictly ergodic systems, we introduce the class of CF-Nil(k) systems: systems for which the maximal measurable and maximal topological k-step pronilfactors coincide as measure preserving systems. We show that the CF-Nil(k) systems are precisely the class of minimal systems for which the k-step nilsequence version of the Wiener-Wintner average converges everywhere. As part of the proof we establish that pronilsystems are coalescent. In addition, we characterize a CF-Nil(k) system in terms of its (k + 1)-th dynamical cubespace. In particular, for k = 1, this provides for strictly ergodic systems a new condition equivalent to the property that every measurable eigenfunction has a continuous version. Joint work with: Yonatan Gutman.

报告人简介:连政星,厦门大学数学科学学院助理教授。2016年毕业于中国科学技术大学,获理学博士学位。先后在加拿大阿尔伯塔大学,波兰科学院数学所从事博士后研究工作。研究方向包括拓扑动力系统,遍历理论,主要研究拓扑动力系统中的幂零系统,以及Sarnak猜测。已在Adv. Math., Ergodic Theory Dynam. Systems, J. Diff. Equ., J. Funct. Anal.等期刊发表论文多篇。