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Linear operators preserving stability and the Lee-Yang program

Date: 
Wednesday 25th June 2008 - 14:00 to 15:00
Venue: 
Center for Mathematical Sciences
Abstract: 

We characterize all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing when the variables are in (products of) prescribed open circular domains, which solves the higher dimensional counterpart of a long-standing classification problem going back to P\'olya-Schur. This also leads to a self-contained theory of multivariate stable polynomials and a natural framework for dealing in a uniform manner with Lee-Yang type problems in e.g. combinatorics, statistical mechanics, complex analysis, which we illustrate with several examples. This is joint work with Petter Brändén.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons