Multivariate Pólya-Schur theory and applications

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• Julius Borcea (Stockholm University)
• Thursday 19 June 2008, 14:30-15:30
• MR14.

If you have a question about this talk, please contact Andrew Thomason.

Linear operators preserving non-vanishing properties are an important tool in e.g. combinatorics, the Lee-Yang program on phase transitions, complex analysis, matrix theory. We characterize all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing when all variables are in a prescribed open circular domain, which solves the higher dimensional counterpart of a long-standing classification problem going back to Pólya-Schur. This leads to a self-contained 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.

This talk is part of the Combinatorics Seminar series.

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