Dynamic Systems Seminar——Smooth ergodic theory, group actions, and the Zimmer Program
主 题: Dynamic Systems Seminar——Smooth ergodic theory, group actions, and the Zimmer Program
报告人: Aaron Brown (University of Chicago)
时 间: 2018-03-27 15:10-17:00
地 点: Room 104, No. 3 Teaching Building
Abstract: I will discuss actions of discrete groups on manifolds—particularly actions of lattices in higher-rank Lie groups such as SL(n, Z)—and introduce and motivate some conjectures about such actions, commonly known as the Zimmer program. I’ll discuss one recent result from joint work with D. Fisher and S. Hurtado showing all actions of SL(n,Z) on (n-2)-manifolds are finite. Along the way, I’ll introduce extensions of tools from smooth ergodic theory to the setting of actions of higher-rank abelian groups which we use in our proof.