Zuo Lin, a mathematician at the University of California, Berkeley, presents this joint IAS/Princeton University Groups and Dynamics Seminar on quantitative versions of Ratner's equidistribution theorem. Ratner's theorem states that for a lattice Gamma in a Lie group G, orbits of a unipotent subgroup U equidistribute in a periodic orbit of some larger subgroup L. Lin reviews why this question is well understood for horospherical subgroups but much harder otherwise, then builds on recent work by Lindenstrauss, Mohammadi, Wang and Yang on one-parameter non-horospherical unipotent groups. The talk's main content is Lin's own extension of these effective equidistribution results to higher dimensional unipotent subgroups, with explicit application to maximal unipotent subgroups of SO(p,q) acting in SLn(R)/SLn(Z). Time permitting, Lin also sketches a submodularity inequality for irreducible representations that serves as a key technical ingredient in the proof. This is a specialist research talk aimed at an audience already fluent in homogeneous dynamics and Lie theory.