SEMINAR: Groups and Combinatorics Seminar: Peter Vandendriessche, 4pm Sep 21 in Weatherburn LT

Speaker: Peter Vandendriessche (Ghent University)

Title: Classification of hyperovals and KM-arcs in small projective planes

Time and place: 4pm Friday 21 Sep 2018, Weatherburn LT

Abstract: Hyperovals (resp. KM-arcs) are point sets in PG(2,q) (resp. in AG(2,q)^D) such that every line contains 0 or 2 of these points. Every hyperoval can be seen as a KM-arc, but not vice versa; both only exist when q is even. Hyperovals always have size q+2, KM-arcs have size q+t for some t|q. A commonly studied problem for any projective substructure is to classify its examples in small projective planes. We give an overview of the known results, with particular focus on the most recent result: a full classification of the KM-arcs in PG(2,64).

(Actually what I write above is not true, since the computations are not finished, but I know they'll finish in a reasonable time and by now it is unlikely that any new examples will pop up.)