The course will serve as an introduction to nonnegative polynomials, sums of squares, and their connection with polynomial optimization via semidefinite programming. We will cover real algebraic geometry topics such as the real Nullstellensatz and Positivstellensatz and their applications in sums of squares approach to polynomial optimization. We will also see how a convex geometry/optimization viewpoint can lead to new results in Real Algebraic Geometry.
Possible special topics and applications include: semidefinite and sums of squares lifts of polytopes with applications to combinatorial optimization, connections to the Unique Games Conjecture, sums of squares on varieties, sums of squares and construction of Lyapunov functions with applications in robotics.
