turkmath.org

I will discuss real algebraic curve with many, but *finitely* many real points. (Clearly, such curves would tend to be singular, e.g., the solitary point $x^2+y^2=0$.) The bulk of my talk will deal with the known upper bounds on the number of points, which are of a purely topological nature. If time permits, I will discuss a few constructions, mainly, for $P^2$ and other rational surfaces. Alas, most constructions used rely upon those of curves with many components (Viro's patchworking, dessins d'enfants, etc.) and, as such, are probably far from perfection.