Resumen de Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation

Dmitry Kleinbock, Georges Tomanov

• The main goal of this work is to establish quantitative nondivergence estimates for flows on homogeneous spaces of products of real and p-adic Lie groups. These results have applications both to ergodic theory and to Diophantine approximation. Namely, earlier results of Dani (finiteness of locally finite ergodic unipotent-invariant measures on real homogeneous spaces) and Kleinbock¿Margulis (strong extremality of nondegenerate submanifolds of Rn) are generalized to the S-arithmetic setting.