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CANCELLED Polynomial time computation in > matrix groups and applications

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GRA - Groups, representations and applications: new perspectives

This talk will be in two parts. In the first part, we discuss a recent joint result with Charles Leedham-Green and Eamonn O'Brien that there is a version of the CompositionTree program for finite matrix groups that runs in polynomial time subject to the availability of oracles for discrete logarithm and integer factorisation. The existence of such an algorithm was established by Babai, Beals and Seress in 2009 but, unlike our new version, their algorithm was not intended for or suitable for practical implementation. In the second part we discuss possible applications of CompositionTree and the related functionality that has been implemented in Magma and GAP . In particular, in his recent PhD thesis at Manchester (supervised by Peter Rowley), Alexander McGaw used the Magma implementations to carry out structural computations in the group E_8(2), with a view to settling remaining uncertainties about its maximal subgroups.




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