中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
综合报告
报告人： 魏达仁 博士（新加坡国立大学）
题 目：Rigidity, complexity and unipotent actions
时 间：2023.07.14（星期五），09:00-10:00
地 点：数学院南楼N913
摘 要：Unipotent flows have some striking rigidity properties: for instance, every orbit is recurrent, and every orbit closure as well as every invariant measure is homogeneous. In particular, the isomorphism rigidity theorem tells us thata measurable isomorphism between two flows in the class of unipotent flows on quotients of semisimple groups implies an algebraic isomorphism between their corresponding groups and lattices. Moreover, such systems always have zero entropy and thus they cannotbe distinguished by classical entropy invariants. We extend the isomorphism rigidity for unipotent flows to its time changes. More precisely, one parameter unipotent flows on quotients of semisimple groups fall into two categories: 1. unipotent flows that are time changes of linearirrational flows on T^2 and hence are all time changes of each other; 2. The measurable isomorphism between their time changes implies the much stronger (algebraic) equivalence as above. We also show that the complexity of time changes of unipotent flows canbe described explicitly in terms of the corresponding adjoint action, and associated Jordan block-like structures. Moreover, this is also true for the complexity of high rank abelian unipotent actions.This is based on joint works with Adam Kanigowski, Philipp Kunde, Elon Lindenstrauss and Kurt Vinhage.
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