Séminaires : Séminaire d'Algèbre

There are three families of Coxeter systems: finite, affine, and indefinite. By far, the class of indefinite Coxeter systems (which includes, for instance, hyperbolic discrete reflection groups) is the least understood. One reason is the lack of tools to control the set of reflections, or equivalently, the root system and the Coxeter arrangement. In this talk, I will discuss recent developments of such tools and some open problems involving the notions of Garside shadows (introduced in the context of Artin–Tits monoids) and Shi arrangements. As an example of an application, we will explain their relationship with the Osajda–Przytycki biautomatic structure for Coxeter systems.

This talk will take place in hybrid mode at the Institut Henri Poincaré.