SEMINAR: Groups and Combinatorics Seminar:Serendipity, involutions and regular semisimple matrices


Groups and Combinatorics Seminar:Serendipity, involutions and regular semisimple matrices 
Other events...

Groups and Combinatorics Seminar
Cheryl Praeger
will speak on
Serendipity, involutions and regular semisimple matrices
at 12noon in MLR2 on Tuesday April 20.
Abstract: (joint work with Akos Seress)
Key to studying finite simple groups is to study their involution
centralisers, and this is true also in a computational setting.
In a seminal paper, Chris Parker and Rob Wilson present and analyse a
practical algorithm for computing the centraliser of an involution z
in a finite classical group of odd characteristic. Fundamental to their
approach, using Bray’s theorem and an observation of Richard Parker, is
the estimation of the proportion of pairs of conjugates of z whose
product has odd order  and is regular semisimple. Their analysis
estimates that O(n) random selections are needed to find a suitable
random conjugate of z.
Motivated by the wish to improve on Parker and Wilson's algorithm by
exploiting the pairs of conjugates of z whose product has even order,
we were led by experimental evidence to estimate the proportion of such
pairs whose product is regular semisimple. Serendipity came to our
rescue: we recognised a probability generating function for estimating
such pairs as similar to one analysed by Jason Fulman, Peter Neumann and
me for computing the proportion of separable matrices in unitary groups.
A similar analysis enabled us find the limiting proportion, depending
only on the field size q, for general linear groups and to prove
exponentially fast convergence.
Speaker(s) 
Cheryl Praeger

Location 
Maths Lecture Room 2


Contact 
Michael Giudici
<[email protected]>

Start 
Tue, 20 Apr 2010 12:00

End 
Tue, 20 Apr 2010 12:45

Submitted by 
Michael Giudici <[email protected]>

Last Updated 
Thu, 15 Apr 2010 17:09

Included in the following Calendars: 

 Locations of venues on the Crawley and Nedlands campuses are
available via the Campus Maps website.
 Download this event as:
Text 
iCalendar

Mail this event:
