##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Zuo Lin

#### UCSD

## Distribution of dense lattice orbits on homogeneous spaces

##### Abstract:

Let $H < G$ both be noncompact connected semisimple real algebraic groups and $\Gamma < G$ be a lattice. In the work of Gorodnik--Weiss, they showed that the distribution of dense $\Gamma$-orbit on homogeneous space $G/H$ is asymptotically the same as $G$-orbit on $G/H$. One key ingredient in their proof is Shah's theorem derived from the famous Ratner's theorem. In this talk, we report an effective version of this result in the case $(G, H, \Gamma) = (\mathrm{SL}_3(\mathbb{R}), \mathrm{SO}(2, 1), \mathrm{SL}_3(\mathbb{Z}))$. The proof uses recent progress by Lindenstrauss--Mohammadi--

Host: Brandon Seward

### December 7, 2023

### 10:00 AM

APM 7321

Research Areas

Ergodic Theory and Dynamical Systems****************************