88直播

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88直播-真人直播 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