Han Yu

Gallagher on possibly flat hypersurfaces

We will consider Gallagher's theorem on multiplicative diophantine approximation. It says that with respect to the Lebesgue measure, almost all points satisfy a certain dichotomy regarding multiplicative diophantine approximation. It is an open question whether or not such a property holds not only for the Lebesgue measure but also for other 'well-structured' measures, e.g. surface measures on manifolds. We will survey the history of this problem as well as recent results. This talk is based on a joint work with Sam Chow (Warwick).