Lectures on the Kadison-singer Problem

The Kadison-singer Problem in Mathematics and Engineering: a Detailed Account

We will show that the famous, intractible 1959 Kadison-Singer problem in C∗-algebras is equivalent to fundamental unsolved problems in a dozen areas of research in pure mathematics, applied mathematics and Engineering. This gives all these areas common ground on which to interact as well as explaining why each of these areas has volumes of literature on their respective problems without a satis...

A Frame Theory Primer for the Kadison-singer Problem

This is a primer on frame theory geared towards the parts of the theory needed for people who want to understand the relationship between the Kadison-Singer Problem and frame theory.

Interlacing Families and the Kadison–Singer Problem Contents

Frames and the Kadison-singer Problem: a Report for Aim

This is an introduction to the problems connecting frame theory and the Kadison-Singer Problem. 1. Overview For an extensive introduction to the aspects of frame theory needed for an understanding of the Kadison-Singer Problem we refer to the survey paper [3], which is posted in this section of the web page “The Kadison-Singer Problem”. In the following section we will just give the basic defin...

Ramanujan Graphs and the Solution of the Kadison–Singer Problem

We survey the techniques used in our recent resolution of the Kadison– Singer problem and proof of existence of Ramanujan Graphs of every degree: mixed characteristic polynomials and the method of interlacing families of polynomials. To demonstrate the method of interlacing families of polynomials, we give a simple proof of Bourgain and Tzafriri’s restricted invertibility principle in the isotr...