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Limits of translates of curves on homogeneous spaces and Dirichlet's theorem on Diophantine approximation

Limits of translates of curves on homogeneous spaces and Dirichlet's theorem on Diophantine approximation

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Nimish Shah, Yale University
Fine Hall 601

By proving an equidistribution theorem for certain sequences of expanding translates of smooth measures on curves on homogeneous spaces of $SL(n,R)$, we show that the Dirichlet's theorem on simultaneous diophantine approximation cannot be improved for related quantities in the sense of Davenport and Schmidt.