Polynomial effective equidistribution - Lindenstrauss, Elon; Mohammadi, Amir; Wang, Zhiren (Comptes Rendus. Mathématique)
We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $SL_2(\mathfrak{l})$ in arithmetic quotients of $SL_2(\mathbb{C})$ and $SL_2(\mathfrak{l})× SL_2(\mathfrak{l})$.The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.