SEMINAR: Groups and Combinatorics Seminar: Perpsystems of Projective Spaces


Groups and Combinatorics Seminar: Perpsystems of Projective Spaces 
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Groups and Combinatorics Seminar
John Bamberg (UWA)
will speak on
Perpsystems of Projective Spaces
at 1pm on Tuesday 23 November in MLR2.
Abstract: Perpsystems were introduced by De Clerck, Delanote, Hamilton, and Mathon to construct new partial geometries, and hence, possibly new strongly regular graphs. In a projective space PG(d,q) equipped with a nondegenerate polarity "perp", a perpsystem is a set of mutually disjoint rsubspaces of PG(d,q) such that every pair of elements from this set are mutually opposite (disjoint from the "perp" of the other), and it must have the maximum theoretically possible size. By “pair” here, we do not require that the two elements be distinct, so in particular, every element of a perpsystem is nonsingular with respect to "perp". The only known perpsystems are selfpolar maximal arcs of PG(2,q), q even, and Mathon’s sporadic example in PG(5,3). Mathon’s example had no geometric construction, it was simply written down in coordinate form, but it was known that its stabiliser was isomorphic to S_5 and that it was a perpsystem with respect to a symplectic, hyperbolic and elliptic polarity. We will give an overview of the geometric background necessary to understand perpsystems and present some recent work of De Clerck and the author which provides a geometric construction of Mathon's perpsystem.
All welcome.
Speaker(s) 
John Bamberg

Location 
Maths Lecture Room 2


Contact 
Michael Giudici
<[email protected]>

Start 
Tue, 23 Nov 2010 13:00

End 
Tue, 23 Nov 2010 13:45

Submitted by 
Michael Giudici <[email protected]>

Last Updated 
Thu, 18 Nov 2010 09:17

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