Prof. Bernd Sturmfels

Title: 3264 Conics in a Second

Abstract: This seminar spans a bridge between 19th century geometry to 21st century computing. We start with a classical theme that was featured in the January 2020 issue of the Notices of the American Mathematical Society, namely the 3264 conics that are tangent to five given conics in the plane. We discuss the computation of these conics, by solving a system of polynomial equations with numerical methods that are fast and reliable. In our discussion we will focus on the role of applied algebraic geometry in statistics and optimization, starting from the role of linear spaces of symmetric matrices (LSSM) for Gaussian models and semidefinite programming.