Tuesday, April 2, 2019, 3:00pm
Title: Highlights of the classification of simple nuclear C*-algebras
Abstract: Hyperfinite von Neumann factors were classified over a 40-year span starting with Murray and von Neumann's work in the 1940s, almost completed by Connes in the 1970's, and the last piece done in the mid 1980s with Haagerup's proof that the hyperfinite type III_1 factor is unique. The first systematic work on simple C*-algebras, the natural analog of a von Neumann factor, was done by Glimm in 1959. Glimm's work was extended to the larger class of AF-algebras by Bratteli (late 1960s) and Elliott (mid 1970s). In the late 1980s, Elliott realized that these sporadic classification results had the potential to be extended to a much larger and natural class of C*-algebras, similar to the class of hyperfinite von Neumann factors. The Elliott conjecture set the agenda for much research in C*-algebras the following 30 years, culminating recently with the almost complete classification in terms of K-theory and traces of simple separable nuclear C*-algebras (satisfying a certain regularity property as well as a K-theoretical condition, called the UCT). I will describe some of the highlights of this development.