Alexander Kechris (Caltech)

✒️ TITLE / TITRE

Orbit equivalence relations and the compact action realization problem

📄 ABSTRACT / RÉSUMÉ

The study of orbit equivalence relations induced by Borel actions of countable groups on Polish (separable completely metrizable) spaces, and their orbit spaces, has been a very active area of research for several decades in various fields of mathematics, including ergodic theory, operator algebras, geometric group theory, combinatorics, probability and descriptive set theory. Many results in this area have been obtained using ergodic (measure theoretic) methods. After giving a basic introduction to this theory, I will focus on a new direction of topological nature that deals with the problem of realizing orbit equivalence relations by continuous actions on compact metrizable spaces and in particular subshifts. This also leads to considering a natural universal space for such actions and equivalence relations via subshifts and originates the study in this space of various important classes, especially the so-called hyperfinite ones, which are those induced by actions of the group of integers. This is joint work with Josh Frisch, Forte Shinko and Zoltan Vidnyánszky.

📍 PLACE / LIEU 
Hybride - CRM, Salle / Room 5340, Pavillon André Aisenstadt