Ramanujan Graphs and the Solution of the Kadison-Singer Problem
  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. 
Adam W. Marcus, Daniel A. Spielman, Nikhil Srivastava
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