Igor Klep (Ljubljana)

Connes' Embedding Conjecture

Abstract.
The embedding conjecture was formulated by A. Connes in the seventies.
It asks whether any finite type II_1-factor von Neumann algebra can be
embedded into the ultrapower of the hyperfinite II_1-factor, and is one
of the most important open problems in operator algebras.
In this talk we shall explain all the notions involved in the conjecture
and show how it can be rephrased as a problem on positive noncommutative
polynomials.