Abstract:
This
talk is about the results of my thesis which generalizes one result of
D.Kleinbock and G. Margulis on metric Diophantine
approximation
with dependent quantities to so called "simultaneous Diophantine
approximation" of a system of linear forms. In particular,
we
establish "joint strong extremality" of arbitrary finite collection of
smooth nondegenerate submanifolds of $\R^n$.