Orbit Equivalence Theory, Cost, Ergodic Dimension and L2 Betti Numbers - Lecture 3

Explore the third lecture in a series on orbit equivalence theory, cost, ergodic dimension, and L2 Betti numbers presented by Damien Gaboriau at the Centre de recherches mathématiques (CRM). Delve into the foundations of measured group theory, a 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. Investigate 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 various examples, tackle 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 67-minute presentation, part of the Measured Group Theory program held in March 2023.