Colloquium: "A 'Quantum' Ramsey Theorem for Operator Systems"

Abstract: Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under the formation of Hermitian adjoints.  I claim that if n is sufficiently large then there exists a rank k orthogonal projection P such that dim(PVP) = 1 or k^2.
 

I will explain the statement of the theorem in more detail and talk about why it is "quantum" and how it relates to Ramsey's classic theorem about graphs.  Then I will describe some of the ideas that go into the proof.

Host: John McCarthy

Tea @ 3:45 in Cupples I, Room 200