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The solution of the Kadison-Singer Problem

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  • UserDaniel Spielman (Yale)
  • ClockMonday 01 June 2015, 17:00-18:00
  • HouseMR2, CMS.

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In 1959, Kadison and Singer posed a problem in operator theory that has reappeared in many guises, including the Paving Conjecture, the Bourgain-Tzafriri Conjecture, the Feichtinger Conjecture, and Weaver’s Conjecture. I will explain how we solve the Kadison-Singer Problem by proving Weaver’s Conjecture in Discrepancy Theory.

I will explain the “method of interlacing polynomials” that we introduced to solve this problem, and sketch the major steps in the proof. These are the introduction of “mixed characteristic polynomials”—-the expected characteristic polynomials of a sum of random symmetric rank-1 matrices, the proof that these polynomials are real rooted, and the derivation of an upper bound on their largest roots.

These techniques are elementary, and should be understandable to a broad mathematical audience.

This is joint work with Adam Marcus and Nikhil Srivastava.

A wine reception will follow the talk in the Central Core, CMS

This talk is part of the Mordell Lectures series.

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