Mathematics

The Varchenko determinant is defined on hyperplane arrangement. It was a general formula which can be written in a more explicit way on arrangement of real reflection group.
We briefly review  the definition and the general expression of this determinant. Then we mainly present the different aspects of the real reflection groups (in algebra as finite Coxeter groups, in geometry as Coxeter arrangements, and in combinatorics as Coxeter complexes), and how these different aspects interact each other. We finish by talking on the role played by each aspect for the calculation of the Varchenko determinant of any Coxeter arrangement.
This research was done in cooperation with Goetz Pfeiffer from the National University of Ireland, Galway.