Nathan Kaplan Yale University A (k,n)(k,n)-arc of P2(Fq)P2(Fq) is a set of nn rational points in the projective plane, no more than kk of which lie on a line. Segre's famous theorem on (2,n)(2,n)-arcs says that when qq is odd, the largest (2,n)(2,n)-arc is of size q+1q+1 and every such arc is the zero set of a smooth conic. When qq is even there are (2,q+2)(2,q+2)-arcs called hyperovals, which are yet to be completely classified. In addition to asking for the largest size of an arc, we can ask for the number of arcs of a given size. We will explain how counting arcs with a small number of points is related to counting del Pezzo surfaces with many rational points. We will also discuss approaches to constructing large (k,n)(k,n)-arcs based on properties of algebraic curves over finite fields.