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SUMMARY:Multivariate Pólya-Schur theory and applications - Julius Borcea 
 (Stockholm University)
DTSTART:20080619T133000Z
DTEND:20080619T143000Z
UID:TALK11964@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Linear operators preserving non-vanishing properties are an im
 portant tool in e.g. combinatorics\, the Lee-Yang program on phase transit
 ions\, complex analysis\, matrix theory. We characterize all linear operat
 ors on spaces of multivariate polynomials preserving the property of being
  non-vanishing when all variables are in a prescribed open\ncircular domai
 n\, which solves the higher dimensional counterpart of a long-standing cla
 ssification problem going back to Pólya-Schur. This leads to a self-conta
 ined theory of multivariate stable polynomials and a natural framework for
  dealing with Lee-Yang and Heilmann-Lieb type problems in a uniform manner
 . The talk is based on joint work with Petter Brändén.\n
LOCATION:MR14
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