Groups and Dynamics: Topology, Measure, and Borel Structure

Abstract

Over the last couple of decades a major branch of study in groups and dynamics has blossomed around the basic structural themes of measure, topology, and Borelness. While several different currents of research have come to shape this theory, the picture that has emerged is one of a constellation of ideas and methods that cut across all three categories in an often surprisingly coordinated way, with constantly expanding connections to probability and geometric group theory. The workshop aimed to further advance this picture with a focus on a number of topics including hyperfiniteness, ergodic theorems, subgroup dynamics, random walks and the Poisson boundary, percolation, entropy, rigidity, Borel complexity, and genericity and classification in spaces of actions.