@inproceedings{b71281f04d4444209bfa2c45b74c02af,
title = "Ramanujan graphs and the solution of the Kadison-Singer problem",
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 = "Interlacing polynomials, Kadison-Singer, Mixed characteristic polynomials, Mixed discriminants, Ramanujan graphs, Restricted invertibility",
author = "Marcus, {Adam W.} and Spielman, {Daniel A.} and Nikhil Srivastava",
note = "Publisher Copyright: {\textcopyright} ICM 2014.All rights reserved.; 2014 International Congress of Mathematicans, ICM 2014 ; Conference date: 13-08-2014 Through 21-08-2014",
year = "2014",
language = "English (US)",
series = "Proceeding of the International Congress of Mathematicans, ICM 2014",
publisher = "KYUNG MOON SA Co. Ltd.",
pages = "363--386",
editor = "Jang, {Sun Young} and Kim, {Young Rock} and Dae-Woong Lee and Ikkwon Yie",
booktitle = "Invited Lectures",
}