For actions of amenable groups, mean equicontinuity is a natural relaxation of equicontinuity obtained by averaging a metric along orbits. It is well known that every such action admits a maximal mean equicontinuous factor. Motivated by earlier work of Qiu and Zhao, Li and Yu introduced the notion of weak sensitivity in the mean for Z-actions to better understand this factor.

In this talk (joint work with Till Hauser), I will explain this relation is insufficient for actions of non-Abelian groups, and present a refined relation, called the regional mean sensitive relation, and explain why it gives the better picture in this setting. Meanwhile, I will discuss its basic properties and show that mean equicontinuity is equivalent to the absence of non-diagonal regional mean sensitive pairs.
Meeting ID: 852 4277 3200 Passcode: 103121