Effective equidistribution for some one parameter unipotent flows

Source abstract

We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\mathrm{SL}_2 (\mathbb{R})$ in arithmetic quotients of $\mathrm{SL}_2 (\mathbb{C})$ and $\mathrm{SL}_2 (\mathbb{R}) \times \rm{SL}_2(\mathbb{R})$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.