3264 Conics in A Second

This lecture spans a bridge from 19th century geometry to 21st century applications. 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. We conclude with a problem in statistics, namely maximum likelihood estimation for linear Gaussian covariance models.