This project is a collaboration between the University of California, Berkley and UiT The Arctic University of Norway, supported by the Peder Sather Center. The project focuses on the intersection of stability and hyperbolicity of polynomials, which are key notions in various fields of mathematics, including combinatorics, optimization, and differential equations. This area investigates the geometric properties of the sets of polynomials whose zeros satisfy certain conditions (e.g., all zeros are real, or all zeros lie in the left half-plane).