A profound result of modern harmonic analysis is Stein's spherical differentiation theorem. To the surprise of many, one may prove a spherical ergodic theorem for R^n actions as a corollary to this result.

Based on intuition coming from equidistribution problems in the Euclidean space and the spherical ergodic theorem, Lindenstrauss and Margulis conjectured an effective spherical equidistribution theorem for horospherical actions.

In the talk, I will present a proof of their conjecture, drawing on techniques from the theory of oscillatory integrals from harmonic analysis on one hand and Venkatesh's effective disjointness theorem from homogeneous dynamics on the other.

If time permits, I will mention some other approaches, mostly due to myself, towards this problem, including results regarding singular Bochner-Riesz means and the analogous question for R^n nilflows.
Speaker(s): Asaf Katz (University of Michigan)