Instructor: Dr. Gergely AMBRUS
Course description: In this course, we tackle discrete geometry problems with analytic, linear algebraic and probabilistic methods. We mainly study discrete sets of vectors that are extremal with respect to a prescribed analytic quantity. Most frequently, this is a potential energy function, or a polarization function, hence the vector sets are solutions of a geometric minimax or maximin inequality. We are interested in the asymptotic behaviour of the analytic quantities as well as the geometric structure of the extremizers. In our study, we cover classical topics such as the plank problems, polarization problems, Chebyshev constants, while we also explore modern applications in computer science and related fields.