Ramanujan Graphs and the Solution of the Kadison-Singer Problem
Spectral Theory
2014-08-20 v1 Combinatorics
Operator Algebras
Abstract
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 isotropic case.
Keywords
Cite
@article{arxiv.1408.4421,
title = {Ramanujan Graphs and the Solution of the Kadison-Singer Problem},
author = {Adam W. Marcus and Daniel A. Spielman and Nikhil Srivastava},
journal= {arXiv preprint arXiv:1408.4421},
year = {2014}
}
Comments
A version of this paper will appear in the proceedings of the 2014 International Congress of Mathematicians