The well known theorems of Khintchine and Jarnik in metric Diophantine approximation provide a comprehensive description of the measure theoretic properties of real numbers approximable by rational numbers with a given error. Various generalisations of these fundamental results have been obtained for other settings, in particular, for curves and more generally manifolds. In this talk I will explain my recent Jarnik type results for a parabola in homogeneous settings and for a planar curve in `functional' inhomogeneous settings. These represents the first comprehensive study of its kind in the theory of Diophantine approximation on manifolds.



Mumtaz Hussain

Research Area

University of Newcastle


Wed, 29/04/2015 - 1:30pm


OMB 145 (Old Main Building)