Semiovals in Finite Projective Planes

In a projective plane, a semioval is a set S of points with the property that for each point P of S , there exists a unique line of the plane which meets S in exactly the point P; in other words, S has a unique tangent at each point.

In this talk, we discuss some of the basic theory of semiovals and providing some examples. We then motivate and discuss some of the speaker's recent work in the area, which involves the study and classification of semiovals which admit ``large'' collinear subsets. Finally, we indicate some connections with cryptography.