Abstract
A polynomial is stable if it is nonzero whenever all variables have positive imaginary parts. We describe how linear preservers of stability may be characterized by their symbols, and how this characterization carries over to the space of so called Lorentzian polynomials. We also present a quantitative theorem that describes how the hyperbolicity cone is deformed by a linear preserver of stability.
This talk is based on joint work with Julius Borcea, June Huh and Adam W. Marcus.