Equidistribution of degenerate curves and Dirichlet improvability

Abstract: In the space of 3-lattices, we study the translates of a line segment under a diagonal flow. Sharp conditions for non-divergence and equidistribution will be given. As an application, we will show that Lebesgue-almost every point on a planar line is Dirichlet non-improvable if and only if the line is irrational. This is joint work with Kleinbock, de Saxcé and Shah. Generalizations to higher dimensions will also be discussed (work in progress with Shah).

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar