Breakfast lecture by Mikael Rørdam

TITLE: When matrices almost commute

ABSTRACT: When are almost commuting matrices near to commuting matrices? Voiculescu gave examples of almost commuting unitary matrices that are far away from any commuting matrices. It was for a long time an open problem, originally posed by Halmos, if almost commuting self-adjoint matrices are near to commuting self-adjoint matrices. This question was resolved in the positive by Lin in the mid 1990s. With Peter Friis, I simplified Lin's proof; and later there were several further improvements of Lin's proof giving quantitative estimates. I will explain some of these results and their proofs.

Coffee and croissants will be served.