Selected Publications

Schottky presentations of positive representations

We show that the notion of 3-hyperconvexity on oriented flag manifolds defines a partial cyclic order. Using the notion of interval given by this partial cyclic order, we construct Schottky groups and show that they correspond to images of positive representations in the sense of Fock and Goncharov. We construct polyhedral fundamental domains for the domain of discontinuity that these groups admit in the projective space or the sphere, depending on the dimension.
preprint

Schottky groups and maximal representations

We describe a construction of Schottky type subgroups of automorphism groups of partially cyclically ordered sets. We apply this construction to the Shilov boundary of a Hermitian symmetric space and show that in this setting Schottky subgroups correspond to maximal representations of fundamental groups of surfaces with boundary. As an application, we construct explicit fundamental domains for the action of maximal representations into $Sp(2n,R)$ on $RP^{2n−1}$.
Geometriae Dedicata

Recent Publications

• Schottky presentations of positive representations

• Rank 1 character varieties of finitely presented groups

• Einstein tori and crooked surfaces

• Schottky groups and maximal representations

Contact

• jburelle (at) ihes.fr
• Bureau 1N2, IHES, 35 Route de Chartres, Bures-sur-Yvette, 91440, France