Orbit Equivalence Theory: Cost, Ergodic Dimension, and L2 Betti Numbers - Part I

Explore the foundations of measured group theory in this comprehensive lecture on orbit equivalence theory, cost, ergodic dimension, and L2 Betti numbers. Delve into the measurable analogue of geometric group theory, introduced by Gromov in the 1990s, focusing on the study of countable group actions that preserve finite measures. Examine 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). Gain insights into L2 Betti number theory and its connection to ergodic dimension. Encounter numerous examples, engage with exercises designed for non-specialists, and discover open problems in the field. Enjoy animated visuals that support intuitive understanding of complex concepts in this engaging presentation by Damien Gaboriau, part of the Measured Group Theory program at the Centre de recherches mathématiques.