The Kadison-Singer Problem

TL;DR

This paper provides a comprehensive overview of the Kadison-Singer problem, its connections across multiple mathematical disciplines, and discusses the recent solution by Marcus, Spielman, and Srivastava.

Contribution

It offers a self-contained presentation of the problem and its related results, highlighting the interdisciplinary impact and recent resolution.

Findings

Kadison-Singer problem was recently solved.

The problem connects various mathematical fields.

The paper consolidates related results and implications.

Abstract

We give self-contained presentation of results related to the Kadison-Singer problem, which was recently solved by Marcus, Spielman, and Srivastava. This problem connects with unusually large number of areas including: operator algebras (pure states), set theory (ultrafilters), operator theory (paving), random matrix theory, linear and multilinear algebra, algebraic combinatorics (real stable polynomials), algebraic curves, frame theory, harmonic analysis (Fourier frames), and functional analysis.