Regularity conditions of dynamical systems and of their crossed products.

par Andrea Vaccaro (ICJ Lyon 1)

mardi 30 sept. 2025, 11:15 → 12:15 Europe/Paris

Fokko (ICJ)

Crossed products C*-algebras provide a canonical construction associating a C*-algebra to a given action of a discrete group on a compact Hausdorff space. With the completion of the so-called Elliott classification program, significant effort has been devoted to understanding how regularity conditions of dynamical systems translate into the corresponding crossed products, with the aim of isolating classes of dynamical systems whose crossed products are regular enough to be classified by means of K-theoretic invariants. After a quick overview, I will present some recent results where, in collaboration with Kospacheilis, Liao, and Tikuisis, we investigate the opposite question—namely, how specific forms of regularity of a crossed product affects the originating dynamical system. Later, I will discuss some important consequences of this for the study of amenable C*-algebras.