# OA seminar: George A Elliott

Speaker: George Elliott (University of Toronto).

Title: The classification of well-behaved simple separable amenable C*-algebras

Abstract: For von Neumann algebras, the adjective "well-behaved" is redundant. For C*-algebras, it refers to a very robust concept, crystallized in the now almost completely established Toms-Winter conjecture, which, as shown by examples of Villadsen, Rørdam, and Toms, is a decidedly restrictive adjunction to amenability. Within this proper subclass (what might be called the Toms-Winter simple separable amenable C*-algebras), the naive invariant (generalizing in a straightforward way that first used for AF algebras) is complete. (This assumes the Universal Coefficient Theorem, which for amenable separable C*-algebras may be redundant.) The proof, developed over more than fifty years (an important part consolidating twenty-five years ago), incorporates large parts of the history of the field.