20.08.2019 um 16:15 Uhr in 69/125:
Vincent Delecroix (LaBRI Bordeaux)
Dirichlet domain computation for real hyperbolic groups
A real hyperbolic group of dimension d is a discrete subgroup of SO(1,d) (the special orthogonal group of a quadratic form of signature (1,d) seen as the isometry group of the real hyperbolic space of dimension d). The main studied cases are d=2,3 which are the so-called Fuchsian and Kleinian groups.
In various situations, one has access to generators of a real hyperbolic group and would like to study its properties (e.g. find relations among the generators). A possible approach for this problem is the construction of a fundamental domain with respect to its action on the hyperbolic space. The Dirichlet fundamental domain is a systematic way to construct one.
After introducing the problem, I will provide several motivating examples. Then, I will discuss the algorithmic part which involves the incidence geometry of polyhedral cones and quadratic optimization (over number fields).