SEMINAR: Groups and Combinatorics Seminar:Hemisystems of generalised quadrangles

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