Homogeneous dynamics and number theory

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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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