Corpus ID: 14187435

Ramanujan Graphs and the Solution of the Kadison-Singer Problem

@article{Marcus2014RamanujanGA,
  title={Ramanujan Graphs and the Solution of the Kadison-Singer Problem},
  author={Adam Marcus and Daniel A. Spielman and Nikhil Srivastava},
  journal={arXiv: Spectral Theory},
  year={2014}
}
  • Adam Marcus, Daniel A. Spielman, Nikhil Srivastava
  • Published 2014
  • Mathematics
  • arXiv: Spectral Theory
  • 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. 

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