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

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).