Title: Bad approximation and exceptional sets in homogeneous dynamics
Speaker: Jim Tseng
Speaker Info: Ohio State
There is a well-known correspondence between the approximation of real numbers by rational numbers and a diagonal flow on the space of unimodular lattices. The set of real numbers that are badly approximable is forced to be measure zero by ergodic theory. However, this set is, nevertheless, large: for example, intersect it with a countable number of isometries of itself and the result has Hausdorff dimension one. This conclusion follows immediately from W. Schmidt’s theorem (1966).Date: Tuesday, May 17, 2011
A suitable generalization of Schmidt’s theorem to systems of affine forms was conjectured in the nineties by D. Kleinbock. I show that a strengthening of the conjecture and various related results hold (joint with M. Einsiedler).