报告人：Mumtaz Hussain（澳大利亚La Trobe大学讲师）

报告题目：The generalised Baker-Schmidt problem on hypersurfaces

报告摘要：The Generalised Baker--Schmidt Problem (1970) concerns the $f$-dimensional Hausdorff measure of the set of $\psi$-approximable points on a nondegenerate manifold. There are two variants of this problem, concerning simultaneous and dual approximation. Beresnevich--Dickinson--Velani (in 2006, for the homogeneous setting) and Badziahin--Beresnevich--Velani (in 2013,  for the inhomogeneous setting) proved the divergence part of this problem for dual approximation on arbitrary nondegenerate manifolds. The corresponding convergence counterpart represents a major challenging open question and the progress thus far has only been attained for a small class of manifolds. In this talk, I will briefly explain my recent solutions to this problem for a planar curves (in particular a parabola) and on hypersurfaces for inhomogeneous approximations and with a non-monotonic multivariable approximating function.

报告时间：2018年4月4日（星期三）上午11:00-12:00

报告地点：科技楼南楼602