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.
%0 Book Section
%1 marcus14
%A Marcus, Adam W.
%A Spielman, Daniel A.
%A Srivastava, Nikhil
%B Proceedings of the international Congress of Mathematicians
%D 2014
%K bipartite determinant interlacing kadison.singer laguerre lift multilinear polynomial ramanujan real-rooted root-free
%P 363--386
%T Ramanujan Graphs and the Solution of the Kadison–Singer Problem
%V 3
%X 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.
@incollection{marcus14,
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.},
added-at = {2016-04-14T02:05:09.000+0200},
author = {Marcus, Adam W. and Spielman, Daniel A. and Srivastava, Nikhil},
biburl = {https://www.bibsonomy.org/bibtex/273f0ad37c26d7a949ea0b345d1b9fcdb/ytyoun},
booktitle = {Proceedings of the international Congress of Mathematicians},
interhash = {c733e0d0ef17e604ee13f7723faaaee0},
intrahash = {73f0ad37c26d7a949ea0b345d1b9fcdb},
keywords = {bipartite determinant interlacing kadison.singer laguerre lift multilinear polynomial ramanujan real-rooted root-free},
pages = {363--386},
timestamp = {2017-12-10T08:35:39.000+0100},
title = {{Ramanujan} Graphs and the Solution of the {Kadison–Singer} Problem},
volume = 3,
year = 2014
}