Ramanujan graphs and the solution of the Kadison-Singer problem

Adam W. Marcus, Daniel A. Spielman, Nikhil Srivastava

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationInvited Lectures
EditorsSun Young Jang, Young Rock Kim, Dae-Woong Lee, Ikkwon Yie
PublisherKYUNG MOON SA Co. Ltd.
Pages363-386
Number of pages24
ISBN (Electronic)9788961058063
StatePublished - 2014
Event2014 International Congress of Mathematicans, ICM 2014 - Seoul, Korea, Republic of
Duration: Aug 13 2014Aug 21 2014

Publication series

NameProceeding of the International Congress of Mathematicans, ICM 2014
Volume3

Conference

Conference2014 International Congress of Mathematicans, ICM 2014
CountryKorea, Republic of
CitySeoul
Period8/13/148/21/14

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Interlacing polynomials
  • Kadison-Singer
  • Mixed characteristic polynomials
  • Mixed discriminants
  • Ramanujan graphs
  • Restricted invertibility

Fingerprint Dive into the research topics of 'Ramanujan graphs and the solution of the Kadison-Singer problem'. Together they form a unique fingerprint.

  • Cite this

    Marcus, A. W., Spielman, D. A., & Srivastava, N. (2014). Ramanujan graphs and the solution of the Kadison-Singer problem. In S. Y. Jang, Y. R. Kim, D-W. Lee, & I. Yie (Eds.), Invited Lectures (pp. 363-386). (Proceeding of the International Congress of Mathematicans, ICM 2014; Vol. 3). KYUNG MOON SA Co. Ltd..