# Mathematical Sciences Research Institute

Home » GAAHD Postdoc Seminar: Pointwise equidistribution for one-parameter diagonal group action on $X=SL_n(\mathbb R)/SL_n(\mathbb Z)$

# Seminar

GAAHD Postdoc Seminar: Pointwise equidistribution for one-parameter diagonal group action on $X=SL_n(\mathbb R)/SL_n(\mathbb Z)$ February 20, 2015 (11:45 AM PST - 12:30 PM PST)
Parent Program: Geometric and Arithmetic Aspects of Homogeneous Dynamics MSRI: Simons Auditorium
Speaker(s) Ronggang Shi (Xiamen (Amoy) University)
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Video
Abstract/Media

Let $F=\{g_t\}$ be a one-parametr diagonal subgroup of $SL_n(\mathbb R)$.

We assume  $F$ has no nonzero invariant vectors in $\mathbb R^n$.

Let $x\in X, \varphi\in C_c(X)$ and $\mu$ be the probability Haar measure

on $X$. For certain proper subgroup $U$ of the unstable horospherical  subgroup

of $g_1$ we show that for almost every $u\in U$

$\frac{1}{T}\int_0^T\varphi({g_tux})dt \to \int_X\varphi d\mu.$

If $\varphi$ is moreover smooth, we can get an  error rate of the convergence.

The error rate is ineffective due to the use of Borel-Cantelli lemma.