Colloquium - Josephine Yu - Positively Hyperbolic Varieties, Tropicalization, and Positroids
Title: Positively Hyperbolic Varieties, Tropicalization, and Positroids
Speaker: Josephine Yu (Georgia Tech)
Abstract: A multivariate complex polynomial is called stable if any line in a positive direction meets its zero set only at real points. Stable polynomials are related to matroids and hyperbolic programming and have applications in theoretical computer science and optimization. We will discuss a generalization of stability to complex algebraic varieties of codimension larger than one and study their combinatorial structure using tropical geometry. We show that their tropicalization are closely related to braid hyperplane arrangements and positroids (matroid arising from the nonnegative part of the Grassmannian) and that their Chow polytopes are generalized permutohedra. This is based on joint work with Felipe Rincón and Cynthia Vinzant.
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