Geodesic
Interlacing families II: Mixed characteristic polynomials and the Kadison–Singer problem
Adam W. Marcus1 ; Daniel A. Spielman1 ; Nikhil Srivastava2
1 Yale University, New Haven, CT
2 Microsoft Research, Bangalore, India
Annals of mathematics, Tome 182 (2015) no. 1, pp. 327-350.

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We use the method of interlacing polynomials introduced in our previous article to prove two theorems known to imply a positive solution to the Kadison–Singer problem. The first is Weaver’s conjecture $\mathrm{KS}_{2}$, which is known to imply Kadison–Singer via a projection paving conjecture of Akemann and Anderson. The second is a formulation due to Casazza et al. of Anderson’s original paving conjecture(s), for which we are able to compute explicit paving bounds. The proof involves an analysis of the largest roots of a family of polynomials that we call the “mixed characteristic polynomials” of a collection of matrices.
DOI : 10.4007/annals.2015.182.1.8

Adam W. Marcus 1 ; Daniel A. Spielman 1 ; Nikhil Srivastava 2

1 Yale University, New Haven, CT
2 Microsoft Research, Bangalore, India 
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Adam W. Marcus; Daniel A. Spielman; Nikhil Srivastava. Interlacing families II: Mixed characteristic polynomials  and the Kadison–Singer problem. Annals of mathematics, Tome 182 (2015) no. 1, pp. 327-350. doi : 10.4007/annals.2015.182.1.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.182.1.8/

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