SEMINAR: Groups and Combinatorics Seminar:Hemisystems of generalised quadrangles


Groups and Combinatorics Seminar:Hemisystems of generalised quadrangles 
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Groups and Combinatorics Seminar
John Bamberg (UWA)
will speak on
Hemisystems of generalised quadrangles
at 12 noon in MLR2 on Tuesday 2 March
Abstract: (Joint work with Michael Giudici and Gordon Royle). A
hemisystem of a generalised quadrangle is a set of half the lines of
the generalised quadrangle such that every point is on a constant
number m of lines. (So necessarily, m is half the number of lines on
any point). The generalised quadrangles of interest are those which
meet the HigmanSims bound, whereby a hemisystem naturally produces a
partial quadrangle and strongly regular graph. Segre (1965) showed
that there exists a hemisystem of the classical generalised quadrangle
H(3,3^2), and it was conjectured by J. A. Thas in 1995 that no
hemisystem of H(3,q^2) exists for q>3. Ten years later, Cossidente and
Penttila proved that for every q odd, there exists a hemisystem of
H(3,q^2), and their examples arise from an embedding of a subgeometry
into H(3,q^2) (namely, an elliptic quadric Q(3,q)). The only known
generalised quadrangles with the same parameters of H(3,q^2), q odd,
are the flock generalised quadrangles. We will present in this talk an
improvement of Cossidente and Penttila's results to flock generalised
quadrangles.
All welcome
Speaker(s) 
John Bamberg

Location 
Maths Lecture Room 2


Contact 
Michael Giudici
<[email protected]>

Start 
Tue, 02 Mar 2010 12:00

End 
Tue, 02 Mar 2010 12:45

Submitted by 
Michael Giudici <[email protected]>

Last Updated 
Mon, 01 Mar 2010 08:58

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