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    <title><string language="fre"><![CDATA[Alexander Gorodnik - Diophantine approximation and flows on homogeneous spaces (Part 1)]]></string></title>
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 fundamental problem in the theory of Diophantine approximation is to 
understand how well points in the Euclidean space can be approximated by
 rational vectors with given bounds on denominators. It turns out that 
Diophantine properties of points can be encoded using flows on 
homogeneous spaces, and in this course we explain how to use techniques 
from the theory of dynamical systems to address some of questions in 
Diophantine approximation. In particular, we give a dynamical proof of 
Khinchin’s theorem and discuss Sprindzuk’s question regarding 
Diophantine approximation with dependent quantities, which was solved 
using non-divergence properties of unipotent flows. In conclusion we 
explore the problem of Diophantine approximation on more general 
algebraic varieties.]]></string></description>
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TZ:+0200
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            <date><dateTime>2013-06-24</dateTime></date>
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