Equidistribution of expanding translates of curves in homogeneous spaces and its application to Diophantine approximation
主 题: Equidistribution of expanding translates of curves in homogeneous spaces and its application to Diophantine approximation
报告人: 杨磊 博士 (Hebrew University of Jerusalem)
时 间: 2015-09-18 16:30 - 17:30
地 点: 理科一号楼1479
We consider an analytic curve \varphi: I \rightarrow \mathbb{M}(n\times m, \mathbb{R}) \hookrightarrow \mathrm{SL}(n+m, \mathbb{R}) and embed it into some homogeneous space G/\Gamma, and translate it via some diagonal flow A=\{a(t): t > 0 \} < \mathrm{SL}(n+m,\mathbb{R}). Under some geometric conditions on \varphi, we prove the equidistribution of the evolution of the translated curves a(t)\varphi(I) in G/\Gamma as t \rightarrow \infty. As an application, we prove that for almost all points on the curve, the Dirichlet's theorem can not be improved. This is a joint work with Nimish Shah.
