The Kadison-Singer problem was a longstanding open problem in functional analysis regarding the extension of certain functionals on C* algebras. The statement was widely believed to be false, but was proved true by Marcus, Speilman and Srivastava in 2013. Their proof used the properties of real stable polynomials to yield unexpected results for random matrices, such as a nonlinear first moment method and control of the mean characteristic polynomial. In this talk, we will outline the proof and use the tools of MSS to prove an intermediate result - the Paving conjecture, from which Kadison-Singer follows.
Speaker(s): Yan Shuo Tan (University of Michigan)