CARMA ANALYSIS AND NUMBER THEORY SEMINAR

Speaker: Dr Mumtaz Hussain (La Trobe University)
Title: Measure theoretic results for small linear forms
Time & Date: 3:00 pm EST, Tuesday 10 September 2013
Venue: Room V205, Mathematics Building, Callaghan Campus, The University of Newcastle
Also available on the Access Grid network (venue: UNewcastle).

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.

This talk will be broadcast using Access Grid Technology from The University of Newcastle. To participate in this seminar, book your University's AGR or a university/APAC etc. AGR that you are otherwise able to use. A listing of Access Grid nodes is available at: http://www.accessgrid.org/nodes.

This seminar notice is available on the AMSI Website: Events > AGR Events

Seminar Convenors

• Liangjin Yao liangjinyao@gmail.com
• Matthew Tam matthew.tam@uon.edu.au

If you (and your colleagues) wish to participate, please:

1. book your own AGR (or university/APAC etc. AGR that you otherwise are able to use), and ask your AGR technical people to use the new AG venue named CARMA (under the pre-existing UNewcastle venue), or contact David Allingham David.Allingham@newcastle.edu.au (the AGR technical person at Newcastle University) in advance of the seminar.
2. Advise the seminar convenor: Liangjin Yao (liangjinyao@gmail.com or: Matthew Tam

(matthew.tam@uon.edu.au)

Contact:

Ms Maaike Wienk
Access Grid Coordinator
Australian Mathematical Sciences Institute
Building 161, C/- The University of Melbourne, Victoria 3010 Australia
P: 03 8344 1776 | F: 03 9349 4106
E: agr@amsi.org.au | W: http://www.amsi.org.au/