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Completely log-concave polynomials and matroids

Startdatum: 02.07.2019 - 16:00
Enddatum: 02.07.2019 - 17:30
Adresse: MZH 6210
Organisator/Ansprechpartner: Prof. Jens Rademacher, Prof. Christine Knipping, (0421) 218-63745, (0421) 218-63721
  • Prof. Cynthia Vinzant / North Carolina State University

Stability is a multivariate generalization for real-rootedness in univariate
polynomials. Within the past ten years, the theory of stable polynomials has
contributed to breakthroughs in combinatorics, convex optimization, and
operator theory. I will introduce a generalization of stability, called complete
log-concavity, that satisfies many of the same desirable properties. These
polynomials were inspired by work of Adiprasito, Huh, and Katz on
combinatorial Hodge theory, but can be defined and understood in
elementary terms. The structure of these polynomials is closely tied with
notions of discrete convexity, including matroids, submodular functions, and
generalized permutohedra. I will discuss the beautiful real and combinatorial
geometry underlying these polynomials and applications to problems in
matroid theory. This is based on joint work with Nima Anari, Kuikui Liu, and
Shayan Oveis Gharan.
                                                                                       Einladung von Prof. King