Orbit Equivalence Theory, Cost, Ergodic Dimension and L2 Betti Numbers - Lecture 2

Explore the second part of a comprehensive lecture on orbit equivalence theory, cost, ergodic dimension, and L2 Betti numbers in measured group theory. Delve into the foundations of this measurable analogue of geometric group theory, introduced by Gromov in the 1990s. Examine the study of countable group actions preserving finite measures, with a focus on orbit equivalence. Discover key invariants in the field, including the theory of cost (a measured analog of group rank) and ergodic dimension (a measured analog of geometric group dimension). Investigate the connection between ergodic dimension and L2 invariants, necessitating an exploration of L2 Betti number theory. Encounter various examples and tackle exercises designed to provide non-specialists with insights into the field. Engage with open problems in measured group theory and enjoy intuition-supporting animated visuals throughout the presentation.