Metric Diophantine approximation: well approximable theory on manifolds

Speaker: 

Mumtaz Hussain

Affiliation: 

University of Newcastle

Date: 

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

Venue: 

OMB 145 (Old Main Building)

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.

School Seminar Series: