Orateurs

• Maria Montanucci (Technical University of Denmark) : Maximal curves over finite fields
• Philippe Moustrou (Université Toulouse Jean Jaures) : From Weil to Oesterlé making a detour by Serre: Upper bounds on the number of rational points of curves over finite fields

Emploi du temps et programme prévisionnel 

Jeudi 29 janvier

• 14h - 15h : Maria Montanucci 1
  Basic definitions: Algebraic varieties (affine/projective) vs algebraic function fields, divisors and Riemann-Roch Spaces, Riemann's theorem and genus of an algebraic curve.
• 15h15 - 16h15 : Philippe Moustrou 1 
  Weil's bound: introduction of the Zeta function and the connection with the number of points.

Pause café

• 16h45 - 17h45 : Maria Montanucci 2 
  Maximal curves, definition and examples, focus on the Hermitian curve.

Vendredi 30 janvier

• 9h - 10h : Philippe Moustrou 2
  Improving Weil's bound: Serre's trick and other bounds for the number of Fq-points of a curve.

Pause café

• 10h30 - 11h30 : Maria Montanucci 3
  Constructing maximal curves, coverings.
• 11h30 - 12h30 : Philippe Moustrou 3
  Using intersection theory to prove Weil's bound, higher order bounds and connection between known bounds.

Pause déjeuner

• 14h - 15h : Maria Montanucci 4
  More recent results and open problems on maximal curves
• 15h15 - 16h15 : Philippe Moustrou 4
  Combining ideas: how to include Serre's trick in higher order bounds, with a concrete focus on Ihara's bound.