MM7054: Nonlinear algebra

The toolbox of linear algebra is often not sufficient to meet the nonlinear world. Polynomials offer a natural generalization. The course offers participants hands-on investigations (via both proofs and coding) of wide classes of algebraic optimization problems and algebraic inverse problems, coming from various fields of engineering (robotics, computer vision, deep learning, etc).

The course covers: Overview of the necessary background in algebra/algebraic geometry. Solving polynomial systems with symbolic and numeric methods, optimization over semi-algebraic sets, tensor geometry, metric algebraic geometry. Applications of the theory to solve problems within engineering, machine learning, data science, AI.