Ivan Dimitrov
Queen’s University, Kingston, Canada

Abstract: Root systems were introduced by Wilhelm Killing in 1889 as a tool for classifying Lie algebras. Since then, they have become ubiquitous, appearing in various contexts in seemingly unrelated areas of Mathematics. In this lecture series, I will introduce and study root systems and will define a generalization of root systems. I will explain how this more general structure applies to various problems, e.g. hyperplane arrangements. Finally, I will introduce and study inversion sets of roots. The exposition will be mostly self-contained, assuming Linear algebra and some Group theory background.

Keywords: Root systems, Coxeter groups, Hyperplane arrangements, Inversion sets of roots.