School of Mathematics and Statistics

Postgraduate research

Research being undertaken by our current postgraduates:

Contact

Brian Corr


Supervisors

Start date

Mar 2009

Submission date

Brian Corr

Thesis

Computing in Matrix Groups: Constructive Recognition of Classical Groups

Summary

A group algorithm takes a group G as its input and attempts to answer a question about the structure of G. In particular, we might wish to design recursive algorithms: to identify a normal subgroup N of G, and reduce our questions to questions about the subgroup N and the quotient G/N. In doing so we can {\it recognise} G, that is, find an isomorphism between G and a group in which computations are more easily performed. A key part of this procedure is recognising the Simple Classical Groups.

In 2008, Magaard, O'Brien and Seress found an algorithm to constructively recognise the General Linear Group \GL(d,q) and the Special Linear Group \SL(d,q) in degree at most d^2, by considering separately the three cases that can occur. Our main research question is to find a similar algorithm to recognise the other simple Classical Groups (the Orthogonal, Unitary and Symplectic Groups).

Why my research is important

This project will provide improvements on, and generalisations of, the analyses of existing algorithms for computing in matrix groups, and design new algorithms for constructive recognition of almost simple groups in moderate dimensions.

This work will provide a key component in the worldwide Matrix Group Recognition Project, which aims to provide fast, reliable algorithms for analysing a group input to a computer as matrices.



Statistics clinic

Assistance in statistics is available for Postgraduates students by research at the UWA Centre for Applied Statistics.

 

School of Mathematics and Statistics

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Monday, 16 June, 2014 2:41 PM

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