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CATEGORIES:Mordell Lectures
SUMMARY:The solution of the Kadison-Singer Problem - Danie
l Spielman (Yale)
DTSTART;TZID=Europe/London:20150601T170000
DTEND;TZID=Europe/London:20150601T180000
UID:TALK57468AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/57468
DESCRIPTION:In 1959\, Kadison and Singer posed a problem in op
erator theory that\nhas reappeared in many guises\
, including the Paving Conjecture\, the\nBourgain-
Tzafriri Conjecture\, the Feichtinger Conjecture\,
and Weaver's\nConjecture. I will explain how we
solve the Kadison-Singer Problem by\nproving Weave
r's Conjecture in Discrepancy Theory.\n\nI will ex
plain the "method of interlacing polynomials" that
we\nintroduced to solve this problem\, and sketch
the major steps in the\nproof. These are the int
roduction of "mixed characteristic\npolynomials"--
-the expected characteristic polynomials of a sum
of\nrandom symmetric rank-1 matrices\, the proof t
hat these polynomials are\nreal rooted\, and the d
erivation of an upper bound on their largest\nroot
s.\n\nThese techniques are elementary\, and should
be understandable to a\nbroad mathematical audien
ce.\n\n This is joint work with Adam Marcus and Ni
khil Srivastava.\n\nA wine reception will follow t
he talk in the Central Core\, CMS\n
LOCATION:MR2\, CMS
CONTACT:HoD Secretary\, DPMMS
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