Homogeneous dynamics and number theory

Homogeneous dynamics is another name for the theory of flows on homogeneous  spaces, or homogeneous flows. The study of homogeneous flows has been attracting considerable attention for the last 40-50 years. During the last three  decades it has been realized that some problems in number theory, and in  particular in Diophantine approximation, can be solved using methods from the theory of homogeneous flows. The purpose of the lecture is to give examples of  interactions between homogeneous dynamics and number theory.

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