Unipotent flows on homogeneous spaces of infinite volume

Abstract: M. S. Raghunathan conjectured around 1980 that in a homogeneous space of a Lie group G, with finite volume, any orbit closure of a connected subgroup of G generated by unipotent elements is homogeneous. This conjecture was settled by M. Ratner around 1990. Looking for analogues of Ratner's theorem in the infinite volume setting is a major challenge. For any n>2, we present a family of homogeneous spaces of SO(n,1), with infinite volume, in which we classify all possible orbit closures of any connected subgroup generated by unipotent elements. [This talk is based on joint works with McMullen and Mohammadi (for n=3) and with Minju Lee (for n>3)].

algebraic geometrydifferential geometrygroup theorygeometric topologynumber theory

Audience: general audience

International Conference on Discrete groups, Geometry and Arithmetic

Series comments: Selected participants have been informed through email. Kindly check the 'promotions tab' or the 'spam folder', as some of our emails may land in your spam folder due to bulk emailing from our end.