时间：2026年11月11日（周三）14:00-16:00
地点：E14-116
报告人: 中国科学院，邸睿达
讲座主题：Heights, Positions, and Shapes of Rational Subspaces over Number Fields
讲座摘要: The distribution of rational points of bounded height on algebraic varieties is a centraltheme in Diophantine geometry, closely related to Manin’s conjecture. For Grassmannians,rational points correspond to rational subspaces, leading to classical counting problemsstudied by Schmidt and Thunder. Beyond counting, one can ask finer questions about howthese subspaces are distributed and what geometric shapes arise naturally from them.
In this talk, I will discuss how these questions can be studied using tools from homogeneous dynamics and the geometry of numbers. Building on earlier work of Horesh and Karasik, we establish an effective joint equidistribution theorem over arbitrary number fields, describing simultaneously the positions of rational subspaces and the shapes of their associated subspaces and quotients, with power-saving error terms. I will explain the main ideas behind the proof and discuss applications to classical counting problems in Diophantine geometry.
