Abstract: 

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.

 

Speaker

Mumtaz Hussain

Research Area
Affiliation

University of Newcastle

Date

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

Venue

OMB 145 (Old Main Building)