关于举行澳大利亚拉筹伯大学Mumtaz Hussain 副教授学术报告会的通知

报告题目：The generalised Baker-Schmidt problem (1970) on hypersurfaces

报 告 人：Mumtaz Hussain副教授（澳大利亚拉筹伯大学）

邀 请 人：李 兵教授

报告时间：2018年4月2日（星期一）下午15:00-16:00

报告地点：4号楼4141室

欢迎广大师生前往！

数学学院

  2018年3月28日

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.