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SUMMARY:The solution of the Kadison-Singer Problem - Daniel Spielman (Yale
 )
DTSTART:20150601T160000Z
DTEND:20150601T170000Z
UID:TALK57468@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:In 1959\, Kadison and Singer posed a problem in operator theor
 y that\nhas reappeared in many guises\, including the Paving Conjecture\, 
 the\nBourgain-Tzafriri Conjecture\, the Feichtinger Conjecture\, and Weave
 r's\nConjecture.  I will explain how we solve the Kadison-Singer Problem b
 y\nproving Weaver's Conjecture in Discrepancy Theory.\n\nI will explain th
 e "method of interlacing polynomials" that we\nintroduced to solve this pr
 oblem\, and sketch the major steps in the\nproof.  These are the introduct
 ion of "mixed characteristic\npolynomials"---the expected characteristic p
 olynomials of a sum of\nrandom symmetric rank-1 matrices\, the proof that 
 these polynomials are\nreal rooted\, and the derivation of an upper bound 
 on their largest\nroots.\n\nThese techniques are elementary\, and should b
 e understandable to a\nbroad mathematical audience.\n\n This is joint work
  with Adam Marcus and Nikhil Srivastava.\n\nA wine reception will follow t
 he talk in the Central Core\, CMS\n
LOCATION:MR2\, CMS
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