Fall 2021

A Productization Property/Trick For H-Stable(And Hopefully Strongly Log-Concave) Polynomials

Tuesday, Nov. 30, 2021 2:00 pm3:00 pm

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Leonid Gurvits (City College of New York)


Calvin Lab Auditorium

The simplest homogeneous polynomials with nonnegative coefficients are products of linear forms Prod_{A}(X) associated with nonnegative matrices A. We prove that for any H-Stable(homogeneous and stable) polynomial p with P(E) = 1, where E is the vector of all ones, it's value p(X) = Prod_{A(X)}(X), where A(X) is nonnegative matrix with unit row sums and the vector of column sums equal to the gradient of p at E. I will first explain some intuition, and history, behind the result; sketch the proof and present a few applications and generalizations of this "productization" property. (Joint work with Jonathan Leake).