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SEMINAR: Groups and Combinatorics Seminar:Hemisystems of generalised quadrangles

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Today's date is Wednesday, March 03, 2021
Groups and Combinatorics Seminar:Hemisystems of generalised quadrangles Other events...
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 Higman-Sims 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 sub-geometry 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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