Beyond Linear Algebra

Explore advanced mathematical concepts beyond linear algebra in this 45-minute lecture by Bernd Sturmfels. Delve into recent advancements in computing critical point equations for optimization and statistics, and examine the role of nonlinear algebra in studying linear PDE with constant coefficients. Learn about topics such as nearest points on varieties, Euclidean distance degree, space curves, polyhedral norms, likelihood geometry, Euler characteristic, Schubert calculus, and Cayley's cubic surface. Challenge your understanding of mathematical models and numerical algorithms for solution identification, progressing from undergraduate linear and non-linear algebra to more complex concepts.

Intro
Undergraduate Linear Algebra
Undergraduate Non-Linear Algebral
Nearest Points on Varieties
Euclidean Distance Degree
Space Curves
General Formula
Interpretation
Polyhedral Norms
Likelihood Geometry
Euler Characteristic
Schubert Calculus
Nonlinear Algebra meets Linear PDE
Cayley's Cubic Surface