On effective equidistribution for quotients of SL(d)

TL;DR

This paper establishes the first polynomially effective equidistribution results for closed orbits of semisimple groups with nontrivial centralizer, advancing understanding of homogeneous dynamics.

Contribution

It provides the first effective polynomial rate of equidistribution for certain semisimple group quotients, extending prior theoretical work.

Findings

Proves polynomial effective equidistribution for specific group quotients

Builds on and extends previous work by Einsiedler, Margulis, and Venkatesh

Relies on uniform spectral gap to achieve results

Abstract

We prove the first case of polynomially effective equidistribution of closed orbits of semisimple groups with nontrivial centralizer. The proof relies on uniform spectral gap, builds on, and extends work of Einsiedler, Margulis, and Venkatesh.