Shrinking targets on homogeneous spaces and improving Dirichlet’s Theorem

Group Actions and Dynamics
Event time: 
Monday, November 27, 2017 - 4:15pm to 5:15pm
205 LOM
Dmitry Kleinbock
Speaker affiliation: 
Brandeis University
Event description: 

I will talk about an interesting direction in Diophantine approximation – metric theory for improvements to Dirichlet’s Theorem – which was started by Davenport and Schmidt in the 1960s. We were able to obtain optimal results in the one-dimensional case via continued fractions; while for simultaneous approximation the problem is still open. I will describe a reduction of the problem to dynamics (diagonal flows on the space of lattices), and then talk about an inhomogeneous version, which happens to be easier than the homogeneous one. Joint work with Nick Wadleigh.