December 2
Michał Tomasz Godziszewski,
University of Vienna
Cardinal characteristics of the Calkin algebra and other interactions between logic and operator algebras
In recent years we have been witnessing a dynamic and fertile connection between logic and operator algebras. Many methods from set theory and model theory have been successfully applied to the investigations of $C^\ast$-algebras and other topics in abstract functional analysis (with a brilliant textbook on the 'Combinatorial Set Theory of $C^\ast$-algebras' by I. Farah presenting the current state of the art in this developing field). The purpose of this talk is to provide an introduction to this fruitful interplay with a focus on a certain set-theoretic problem concerning cardinal characteristics of the Calkin algebra which is a structure that may be thought of as a quantum counterpart of the Boolean algebra of subsets of natural numbers modulo finite sets.
Namely, I will present a result concerning possible sizes of families of projections (on a certain Hilbert space) that are mutually pairwise almost orthogonal, which informally means that they are orthogonal modulo 'compact perturbation'. The aforementioned result is joint work with V. Fischer (Vienna).