Responsables : O. Finkel, T. Ibarlucía, A. Khélif, S. Rideau, C. Sureson
Lundi de 15h10 à 16h10, salle 2015 (Attention changement de salle).
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This talk is the second part of Farah’s talk from two weeks ago. From a coarse metric space X one associates a C*-algebra known as the Uniform Roe algebra of X. This algebra has a canonical quotient called the Uniform Roe corona of X. We study the question of what information on spaces X and Y one can infer when the Uniform Roe coronas of X and Y are isomorphic, and how answers to this question depend on the set theoretical axioms in play. This is joint work with Bruno Braga and Ilijas Farah.
Building on recent work of Glasner and Weiss, we will consider a countable group G and define the notion of disjointness between two G-flows X and Y. We then consider the question of when every minimal flow is disjoint from the Bernoulli shift. Time permitting, we will discuss an application of these ideas to an old problem in topological dynamics due to Ellis and/or Furstenberg.
I will start by defining the coarse equivalence of metric spaces. This is an equivalence relation meant to capture the large scale geometry of a given space.
To a coarse metric space one can associate a C*-algebra called uniform Roe algebra.
When does isomorphism of uniform Roe algebras associated imply coarse equivalence of the underlying coarse spaces ? A recent result of Spakula and Willett gives sufficient conditions in the case of coarse metric spaces. These conditions are uniform discreteness and property A (the ‘coarse’ variant of amenability). I will discuss a weakening of these conditions. Very recently, these rigidity results were extended to Roe coronas (quotients of uniform Roe algebras modulo the compact operators). No previous knowledge of coarse spaces, Roe algebras, or logic is required. (This is a joint work with Bruno De Mendoca Braga and Alessandro Vignati.)