Incidence geometry and effective equidistribution in homogeneous dynamics

Abstract: I will explain my proof of an effective version of Ratner’s equidistribution theorem for unipotent orbits in SL(3,R)/SL(3,Z). The proof combines new ideas from harmonic analysis and incidence geometry. In particular, the proof is based on a bootstrapping argument improving the local dimension of measures generated by unipotent orbits. The key is to relate the behavior of the unipotent orbits to a Kakeya model.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar