A dynamical Borel-Cantelli lemma via improvements to Dirichlet's theorem

Dmitry Kleinbock, Shucheng Yu

Let $X\cong {\mathrm{SL}}_2(\mathbb{R})/{\mathrm{SL}}_2(\mathbb{Z})$ be the space of unimodular lattices in ${\mathbb{R}}^2$, and for any $r\ge 0$ denote by $K_r\subset X$ the s…