Speaker: **Karen Strung** (Czech Academy of Science)

Title: Constructions in minimal amenable dynamics and applications to classification of C*-algebras

Time/Date: 4:45-6:15pm, December 14 (Tue.), 2021

Room: This will be an online seminar on Zoom. Please ask Kawahigashi for the Zoom link.

Abstract:
What abelian groups can arise as the K-theory of C*-algebras arising from minimal dynamical systems? In joint work with Robin Deeley and Ian Putnam, we completely characterize the K-theory of the crossed product of a space X with finitely generate K-theory by an action of the integers and show that crossed products by a minimal homeomorphisms exhaust the range of these possible K-theories. We also investigate the K-theory and the Elliott invariants of orbit-breaking algebras. We show that given arbitrary countable abelian groups G_{0} and G_{1} and any Choquet simplex Δ with finitely many extreme points, we can find a minimal orbit-breaking relation such that the associated C*-algebra has K-theory given by this pair of groups and tracial state space affinely homeomorphic to Delta. These results have important applications to the Elliott classification program for C*-algebras. In particular, we make a step towards determining the range of the Elliott invariant of the C*-algebras associated to étale equivalence relations.