** "Geometry and Analysis on Groups" Research Seminar **

For \(G=Z^d\), this connection is quite well understood, but if \(G\) is nonabelian little is known about this connection at present.

The introductory part of this seminar will provide background on algebraic group actions, and the main part will focus on a simple class of modules (those of the form \(M=ZG/ZGf\), where \(ZGf\) is the principal left ideal generated by an element \(f\in ZG\)) and one of the simplest dynamical questions one can ask about such actions: when are they ergodic?

This is joint work with Hanfeng Li and Jesse Peterson.