3264 Conics in A Second

Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given 
instance. This lecture illustrates how these two fields complement each other, especially in the light of emerging new applications. We start with a gem from
the 19th century, namely the 3264 conics that are tangent to five given conics in the plane. Thereafter we turn to current problems in statistics, with focus on 
maximum likelihood estimation for linear Gaussian covariance models.