%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 }