Student Working Seminar in Groups and Dynamics
Date: October 9, 2020
Time: 11:00AM - 12:00PM
Location: Zoom
Speaker: James O'Quinn
Title: Ergodic theorems and amenability
Abstract: Ergodic theorems are one of the main technical cornerstones of ergodic theory, which is the study of dynamical systems from a measurable perspective. Roughly speaking, an ergodic theorem provides a relation between averaging a function over the dynamics and and averaging a function over the space for ergodic systems. Thinking of a dynamical system as a group action on a measure space, the kind of averaging necessary for ergodic theorems to hold happens readily for actions of the integers, but may not be available for other groups. However, amenable groups provide the type of averaging we need. During this talk, I will introduce some of the main ideas in ergodic theory, focusing on the ergodic theorems. I will also relate this to amenable groups, which are objects of great interest in current research and permeate many areas of analysis. No background in dynamics or group theory is assumed for this talk. Newcomers and those with a passing interest in this area are especially encouraged to attend.