Finitary analysis in homogeneous spaces with polynomial rates

Rigidity phenomena in homogeneous spaces have been extensively studied over the past few decades with several striking results and applications. In this talk, we will give an overview of activities pertaining to the quantitative aspect of the analysis in this context. In particular, we will discuss recent density and equidistribution theorems in quotients of $SL_2(\mathbb C)$ and $SL_2(\mathbb R)\times SL_2(\mathbb R)$, which provide a polynomial error rate.  

This is based on joint works with Elon Lindenstrauss and Zhiren Wang.