| 日時 | 2010年1月25日(月) ～ 1月29日(金) |
| 講演者（所属） | Professor Ruth Kellerhals (University of Fribourg) |
| タイトル | Hyperbolic Geometry and Coxeter Groups |
| 概要 | The lectures start with an introduction to spaces of constant curvature and especially to hyperbolic geometry. Among the various models for them, the vector space model is discussed which is best suited for the definition of convex polyhedra and scissors congruence groups. Geometric Coxeter groups as discrete groups generated by finitely many reflections in hyperplanes form the theme of the second lecture. The classification problem and some results are discussed. As an application regular polyhedra, tesselations and constructions of hyperbolic space forms are presented. Several topics will then be covered ranging from sphere packings, horoball geometry and crystallographic groups; Schlaefli's volume differential, polylogarithms and applications; minimal volume problem for hyperbolic space forms with and without cusps; growth of hyperbolic Coxeter groups and arithmetic properties of growth functions. For each theme, exercises and open problems will be presented. |
