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DTSTART:20220313T070000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-william-slofstra-0
SUMMARY:Tutte Colloquium - William Slofstra
CLASS:PUBLIC
DESCRIPTION:TITLE: Positivity and sums of squares in products of free algeb
 ras\n\nSpeaker:\n William Slofstra\n\nAffiliation:\n University of Waterlo
 o\n\nLocation\n MC 5501 or please contact Melissa Cambridge for Zoom link\
 n\nABSTRACT: A noncommutative polynomial is said to be positive relative\n
 to some constraints if plugging matrices (or more generally\, operators\no
 n a Hilbert space) satisfying the constraints into the polynomial\nalways 
 yields a positive operator. It is a natural problem to\ndetermine whether 
 or not a given polynomial is positive\, and if it is\,\nto find some certi
 ficate of positivity. This problem is closely\nconnected with noncommutati
 ve polynomial optimization\, where we want\nto find matrices or operators 
 that maximize the operator norm of some\npolynomial\, subject to the const
 raint that some other polynomials in\nthe operators are positive or vanish
 . When the algebra cut out by the\nconstraints is a free algebra\, free gr
 oup algebra\, or similar algebra\,\nit's well-known that a polynomial is p
 ositive on operators satisfying\nthe constraints if and only if it's a sum
  of Hermitian squares in the\nalgebra.
DTSTAMP:20260413T202006Z
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