Spring 2019

Positively Hyperbolic Varieties

Thursday, May 2, 2019 11:45 am12:30 pm PDT

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Josephine Yu (Georgia Institute of Technology)

Positively hyperbolic varieties are analogues, in higher codimension, of hypersurfaces defined by stable polynomials. They are hyperbolic with respect to the nonnegative Grassmannian, following the notion of hyperbolicity studied by Shamovich, Vinnikov, Kummer, and Vinzant. We show that their tropicalization and Chow polytopes have nice combinatorial structures generalizing the results of Choe, Oxley, Sokal, Wagner, and Brändén on Newton polytopes and tropicalizations of stable polynomials. This is based on joint work with Felipe Rincón and Cynthia Vinzant.