The theory of algebraic curves over finite fields is a very active subject both from a theoretical and an applied point of view. The research school aims to cover theoretical, computational and applied aspects of the topic and thus will be useful to a broad range of students and young mathematicians interested in algebra and its applications.
The research school will develop the subject almost from scratch, beginning from introductory classes on finite fields and algebraic curves. We will cover aspects of the theory of elliptic curves over finite fields as well as the application of the Riemann-Roch theorem to the zeta function of an algebraic curve over a finite field (including the Stepanov- Bombieri-Schmidt proof of the Riemann hypothesis). Applications will also figure prominently with sessions on elliptic curve cryptography, coding theory and computational examples using Pari GP and Sage. Moreover we plan to cover the explicit construction of elliptic curves over finite fields with group of points of large prime order (as needed by cryptographic applications) via complex multiplication. The local organizers are considering conducting a one-week preparatory program for participants who may not be prepared to handle the advanced topics in the research school. Lectures in the preparatory program will be given by local mathematicians.