Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem
Also appears in collection : Homogeneous spaces, diophantine approximation and stationary measures / Espaces homogenes. Approximation diophantienne. Mesures stationnaires
Optimal results on the improvements to Dirichlet's Theorem are obtained in the one-dimensional case. For simultaneous approximation the problem is open. I will describe reduction of the problem to dynamics both in one-dimensional case (via continued fractions) and for higher dimensions (via diagonal flows on the space of lattices). If time allows I'll mention an inhomogeneous version which is easier than the homogeneous one. Joint work with Nick Wadleigh.
