14 June 2011
Venue: Computer Science Room 279, Building 303S
Department of Mathematics seminar by Igor Klep, University of Ljubljana.
The embedding conjecture was formulated by A. Connes in the seventies. It is one of the most important open problems in operator algebras, and asks whether any finite von Neumann algebra can be embedded into the ultrapower of the hyperfinite II_1-factor.
In this talk we shall explain how this characterisation question can be rephrased as a problem on trace-positive noncommutative polynomials. Namely, Connes' conjecture holds if and only if every trace-positive polynomial admits a sum of squares representation with weights. This will give us the opportunity to discuss recent progress on positivity of noncommutative polynomials.
Igor Kelp is an applicant for the Analysis position in the Department; and interested Academic Staff are encouraged to attend.