Geometry Seminar: A. Chalumeau (Strasbourg)
Geometry Seminar (Geometric Analysis)
Speaker: Adam Chalumeau (Strasbourg)
Title: Proper quasi-homogeneous domains of Einstein's universe.
Abstract: Given a bounded domain U within affine space, one can ask if there exist a group of projective automorphisms acting freely and properly discontinuously with compact quotient on U? In that case we say that the domain is divisible. In 1989, Kobayashi proved that divisible domains are always convex. In the early 2000s, Benoist conducted an extensive examination of these ``divisible convex sets'', unearthing a rich variety of ``exotic'' examples. Similar questions arise in other geometric contexts. For instance, in conformal Riemannian geometry, many bounded domains of Euclidean space can be divided by a group of conformal diffeomorphisms. However, in broader geometric frameworks (general flag manifolds), Limbeek and Zimmer conjecture a rigidity result : there should be very few examples of bounded divisible domains. In this presentation, I will show such a rigidity result for pseudo-Riemannian conformal geometry. Specifically, I will establish that any bounded divisible domain of Minkowski space - the pseudo-Riemannian counterpart to Euclidean space - is a diamond. This is joint work with Blandine Galiay.
Speaker: Adam Chalumeau (Strasbourg)
Title: Proper quasi-homogeneous domains of Einstein's universe.
Abstract: Given a bounded domain U within affine space, one can ask if there exist a group of projective automorphisms acting freely and properly discontinuously with compact quotient on U? In that case we say that the domain is divisible. In 1989, Kobayashi proved that divisible domains are always convex. In the early 2000s, Benoist conducted an extensive examination of these ``divisible convex sets'', unearthing a rich variety of ``exotic'' examples. Similar questions arise in other geometric contexts. For instance, in conformal Riemannian geometry, many bounded domains of Euclidean space can be divided by a group of conformal diffeomorphisms. However, in broader geometric frameworks (general flag manifolds), Limbeek and Zimmer conjecture a rigidity result : there should be very few examples of bounded divisible domains. In this presentation, I will show such a rigidity result for pseudo-Riemannian conformal geometry. Specifically, I will establish that any bounded divisible domain of Minkowski space - the pseudo-Riemannian counterpart to Euclidean space - is a diamond. This is joint work with Blandine Galiay.