$C^*$-algebras: structure and classification

Abstract

The theory of $C^*$-algebras traces its origins back to the development of quantum mechanics and it has evolved into a large and highly active field of mathematics. Much of the progress over the last couple of decades has been driven by an ambitious program of classification launched by George A. Elliott in the 1980s, and just recently this project has succeeded in achieving one of its central goals in an unexpectedly dramatic fashion. This Snapshot aims to recount some of the fundamental ideas at play.