Anton Bernshteyn, UCLA
Minimal subdynamics and its applications
Topological dynamics is the study of continuous group actions. The classical and best understood cases are when the acting group is either $\mathbb{Z}$ or $\mathbb{R}$, while the general theory remains far less clear. In particular, the tools to approach the dynamics of non-Abelian discrete groups have only begun to emerge in recent years, in part thanks to the arrival of powerful techniques from combinatorics and descriptive set theory. In this talk, I will illustrate this confluence of ideas by discussing the following very basic problem: If $\Delta$ is a subgroup of $\Gamma$, does $\Gamma$ have a free continuous action on a compact Hausdorff space without nontrivial closed $\Delta$-invariant subsets? This talk is based on joint work with Joshua Frisch.
MC 5501