Applications of $\mathrm{C}^*$-classification

Abstract

We provide some background on the category of classifiable $\mathrm{C}^*$-algebras, whose objects are infinite-dimensional, simple, separable, unital $\mathrm{C}^*$-algebras that have finite nuclear dimension and satisfy the universal coefficient theorem, and describe some applications of the classification of objects in, and morphisms into, this category.Comment: These are lecture notes for the minicourse of the same name delivered during the 2023 Operator Algebras That One Can See Simons Semester at the Institute of Mathematics of the Polish Academy of Science