Cubic surfaces over fields of positive characteristic

The protagonist of this talk is a smooth cubic surface. However, we will be concerned with the most symmetric smooth cubic surfaces, i.e. with smooth cubic surfaces with the largest automorphism group. For an arbitrary field we find the most symmetric smooth cubic surface and show that such a cubic surface is unique up to isomorphism. We discuss in detail the most symmetric smooth cubic surfaces over finite fields of characteristic 2 and what are the challenges in working over such fields. We discuss how the most symmetric smooth cubic surface over the field of two elements helps to find the Jordan constant of the Cremona group of rank 2. Finally, we study the most symmetric smooth cubic surfaces over arbitrary fields of characteristic different from 2.