A subspace theorem for manifolds

Abstract: Schmidt’s subspace theorem is a fundamental result in diophantine approximation and a natural generalization of Roth’s celebrated theorem. In this talk I will discuss a geometric understanding of this theorem that blends homogeneous dynamics and geometric invariant theory. Combined with the Kleinbock-Margulis quantitative non-divergence estimates this yields a natural generalization of the subspace theorem to systems of linear forms that depend nicely on a parameter. I will also present several applications and consequences of the main result. Joint work with Nicolas de Saxcé.

Mathematics

Audience: researchers in the topic

New England Dynamics and Number Theory Seminar