The Solution of the Kadison-Singer Problem

Date

May 2, 2015

Overview

The Kadison-Singer problem is a question in operator theory which
arose in 1959 while trying to make Dirac’s axioms for quantum mechanics
mathematically rigorous in the context of von Neumann algebras.
A positive solution to the problem is given by Nikhil Srivastava by proving essentially the strongest
possible partitioning theorem of this type. The proof is based on two significant
ingredients: a new existence argument, which reduces the problem to bounding
the roots of the expected characteristic polynomials of certain random
matrices, and a general method for proving upper bounds on the roots of such
polynomials. The techniques are elementary, mostly based on tools from the
theory of real stable polynomials

People

  • Portrait of Nikhil Srivastava

    Nikhil Srivastava