TOPICS IN CONVEXITY

INSTRUCTOR: Viorel Nitica, Professor of Mathematics

COURSE DESCRIPTION: We start with introductory topics in topology: topological spaces, Euclidean topology, continuous functions, compact spaces, metric spaces, Heine-Borel theorem. We continue with topics in convexity: Helly, Radon and Caratheodory theorems. We intro- duce convexity in dioids (max-plus and max-min algebra) and discuss segments, semispaces, hemispaces and hyperplanes. For the rest of the course we will read through the book ”Introduction to Geometric Proba- bility”, by Klain and Rota and try to find an analog of Euler formula in higher dimensions.