Equidistribution of Expanding Translates of Curves in Homogeneous Spaces

Explore a mathematical lecture on the equidistribution of expanding translates of curves in homogeneous spaces, presented by Pengyu Yang at the Hausdorff Center for Mathematics. Delve into the study of semisimple connected real algebraic groups and lattices, examining how expanding translates of non-degenerate real-analytic curves under a flow become equidistributed with respect to the Haar measure in G/Γ. Discover the application of this concept to Diophantine approximation on matrices, building upon previous works by N. Shah and L. Yang. Gain insights into the proof methodology, which incorporates Ratner's theorem on measure rigidity for unipotent flows, linearization technique, and a novel approach derived from geometric invariant theory. This hour-long talk, part of the Hausdorff Trimester Program "Dynamics: Topology and Numbers" conference, offers a deep dive into advanced mathematical concepts at the intersection of dynamics, topology, and number theory.