Special Colloquium

Andrew Zucker, University of California San Diego

"Dynamics and Ramsey theory on countable groups and structures"

In topological dynamics, one considers the continuous actions of a topological group on a compact space. We will be most interested in minimal actions, those for which every orbit is dense, and Polish groups, groups whose underlying topology is separable and completely metrizable. When considering the automorphism group of a countable structure, the work of Kechris, Pestov, and Todorcevic establishes a connection between groups whose minimal actions are simple and theorems in finite Ramsey theory. This connection suggests that we view dynamics through a combinatorial lens. On the one hand, we establish dynamical counterparts for infinite Ramsey theorems. This in turn has motivated recent joint work proving many such Ramsey theorems. On the other hand, recent joint work constructing many minimal actions of a countable discrete group can be viewed as a strong "anti-Ramsey" theorem for countable groups.

Zoom link: https://uwaterloo.zoom.us/j/99159090516?pwd=Y1REWmRLd3B4cFhraE1kR0ZTU3JJZz09