Analysis and Probability seminar

Abstract: Recent work of Farah and of Farah–Szabó established a powerful link between absorption properties of non-unital C*-algebras and their coronas (i.e., the quotient of the multiplier algebra by the algebra itself). They showed that if a non-unital C*-algebra tensorially absorbs a strongly self-absorbing C*-algebra, then every relative commutant (by a separable subalgebra) in its corona must contain a unital copy of that strongly self-absorbing algebra. In this talk, I will present a dynamical analogue of this result, establishing a new connection between absorption phenomena and the structure of corona actions. As an intermediate step toward the main theorem, we show that corona actions enjoy what we call the dynamical folding property. This is a strong structural feature that generalises an earlier insight of Phillips and Weaver. All results discussed here are based on joint work with Xiuyuan Li and bor Szabó, available on arXiv.