Nondivergence of reductive group actions on homogeneous spaces

Abstract

Let $G/\Gamma$ be the quotient of a semisimple Lie group $G$ by its arithmetic lattice. Let $H$ be a reductive algebraic subgroup of $G$ acting on $G/\Gamma$. The question we are interested in is whether there is a compact set of $G/\Gamma$ that intersects every H-orbit. We show that the failure of this can be explained by a single algebraic reason, which generalizes several previous results towards this question. We also obtain a way to find this algebraic obstruction, if there is any. This talk is based on joint work with Runlin Zhang.

Speaker

张涵于2021年在美国俄亥俄州立大学取得博士学位，博士生导师为Nimish Shah教授。2021年10月至今在清华大学丘成桐数学科学中心做博士后研究，合作导师为Yitwah Cheung教授，研究方向为齐性动力系统、丢番图逼近等。

divergence of reductive group actions on homogeneous spaces