Time and place: 16:00 Friday 13 May in Blakers LT
Speaker: John Bamberg (UWA)
Title: Hemisystem-like structures in finite geometries
Abstract: This is a longer version of the talk I will be giving at New Directions in Combinatorics (Singapore). Beniamino Segre showed in his 1965 manuscript 'Forme e geometrie hermitiane, con particolare riguardo al caso finito' that there is no way to partition the points of the Hermitian surface H(3,q^2) into lines, when q is odd. Moreover, Segre showed that if there is an m-cover of H(3,q^2), a set of lines covering each point m times, then m=(q+1)/2; half the number of lines on a point. Such a configuration of lines is known as a hemisystem and they give rise to interesting combinatorial objects such as partial quadrangles, strongly regular graphs, and imprimitive cometric Q-antipodal association schemes. This talk will be on developments in the field of hemisystems of polar spaces and regular near polygons and their connections to other interesting combinatorial objects. No background in finite geometry will be assumed.
Speaker: John Bamberg (UWA)
Title: Hemisystem-like structures in finite geometries
Abstract: This is a longer version of the talk I will be giving at New Directions in Combinatorics (Singapore). Beniamino Segre showed in his 1965 manuscript 'Forme e geometrie hermitiane, con particolare riguardo al caso finito' that there is no way to partition the points of the Hermitian surface H(3,q^2) into lines, when q is odd. Moreover, Segre showed that if there is an m-cover of H(3,q^2), a set of lines covering each point m times, then m=(q+1)/2; half the number of lines on a point. Such a configuration of lines is known as a hemisystem and they give rise to interesting combinatorial objects such as partial quadrangles, strongly regular graphs, and imprimitive cometric Q-antipodal association schemes. This talk will be on developments in the field of hemisystems of polar spaces and regular near polygons and their connections to other interesting combinatorial objects. No background in finite geometry will be assumed.