# Séminaires : Séminaire Groupes, Représentations et Géométrie

 Equipe(s) : gr, Responsables : A. Brochier, O. Brunat, J.-Y. Charbonnel, O. Dudas, E. Letellier, D. Juteau, M. Varagnolo, E. Vasserot Email des responsables : Adrien Brochier , Olivier Brunat , Jean-Yves Charbonnel , Olivier Dudas , Emmanuel Letellier , Daniel Juteau , Michela Varagnolo , Eric Vasserot Salle : salle 2015, 2em étage, Adresse : Sophie Germain Description

 Orateur(s) Theodosios DOUVROPOULOS - IRIF, Titre Geometric techniques in Coxeter-Catalan combinatorics Date 12/01/2018 Horaire 10:30 à 11:30 Résume There is a well-known correspondence between simple singularities and (finite, simply laced) Coxeter groups, where the monodromy of the singularity is given by the Coxeter element. Traces of this analogy reach the generality of well-generated groups, the largest class of complex reflection groups that have good analogs of Coxeter elements. In that setting, Bessis generalized the function-theoretic Lyashko-Looijenga morphism to a map (LL) that describes the discriminant hypersurface H of W, via a ramified covering of a points configuration space. There is a natural bijective correspondence (Trivialization Theorem'') between points in a generic fiber of the LL-map, and reduced reflection factorizations of a Coxeter element c of W. This is fundamental in Bessis' work, where the combinatorics of reduced factorizations is used as a recipe to construct the universal covering space of the complement W \ (V - H). However, it relies on an elusive numerological coincidence between the degree of the LL-map and the number of factorizations, that has only been explained in the generality of Weyl groups after work of Jean Michel. We will review various structural properties of the LL map (and, where necessary, develop new ones), produce some finer enumerative results, and propose a uniform approach towards the proof of the Trivialization Theorem.'' Salle salle 2015, 2em étage, Adresse Sophie Germain