SMS scnews item created by Andrew Mathas at Thu 29 Aug 2013 1853
Type: Seminar
Distribution: World
Expiry: 10 Sep 2013
Calendar1: 10 Sep 2013 1500-1600
CalLoc1: AGR Seminar
CalTitle1: AGR Seminar: Measure theoretic results for small linear forms
Auth: mathas@gdh-25.on.site.uni-stuttgart.net in SMS-auth

AGR Seminar

Measure theoretic results for small linear forms

Dr Mumtaz Hussain (La Trobe University)

Host venue
University of Newcastle (CARMA)

Abstract

I will talk about the metrical theory of Diophantine approximation associated with linear forms that are simultaneously small in terms of absolute value rather than the classical nearest integer norm. In other words, we consider linear forms which are simultaneously close to the origin. A complete Khintchine-Groshev type theorem for monotonic approximating functions is established within the absolute value setup. Furthermore, the Hausdorff measure generalization of the Khintchine-Groshev type theorem is obtained. As a consequence we obtain the complete Hausdorff dimension theory. Staying within the absolute value setup, we prove that the corresponding set of badly approximable vectors is of full dimension.

Seminar convenor
Liangjin Yao

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If you would like to attend this seminar in our access grid room then please check to see if the grid is already booked at this time and send an email to accessgridroom@maths.usyd.edu.au to let the CSOs know that you would like to attend.


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