SEMINAR: Groups and Combinatorics Seminar: Jesse Lansdown, 4pm Aug 17 in Weatherburn LT

Speaker: Jesse Lansdown (University of Western Australia/RWTH Aachen)

Title: Hemisystems in Finite Geometries

Time and place: 4pm Friday 17 Aug 2018, Weatherburn LT

Abstract: Given an incidence geometry Γ with elements P called points, and elements L called lines, an m-ovoid O is a subset of P such that every line is incident with exactly m elements of O. If m is exactly half the number of lines on a point, then O is called a hemisystem.

Fr´ed´eric Vanhove showed that the existence of hemisystems in the dual Hermitian polar space implies the existence of new distance-regular graphs with classical parameters, so the existence of hemisystems in this case is of great interest.

In this talk I will define these objects and their geometric settings in greater detail, explain some of the history, and present some recent new results.