Emplacement
Dates
Présentation
The aim of this is school to introduce the participants to the arithmetic and computational aspects of the theory of elliptic curves.
We will develop the theory of elliptic curves from its very beginning also providing an introductory course on algebraic curves and the Riemann Roch theorem. Topics that will be covered include: basic geometric and arithmetic results for elliptic curves over number felds and over fnite felds, the Mordell- Weil theorem for elliptic curves, Galois representations attached to elliptic curves, and the Birch and Swinnerton Dyer Conjecture.
On the computational side we will cover applications of elliptic curves such as the discrete logarithm problem, elliptic curves cryptosystems and the construction of elliptic curve over fnite felds with a prescribed order.
Coordinateurs administratifs et scientifiques
Programme scientifique
Cours 1: "Introduction to algebraic curves ", Elisa LORENZO GARCIA (Université Rennes 1, France)
Cours 2: "Elliptic curves", Christophe RITZENTHALER (Université Rennes 1, France)
Cours 3: "Elliptic curves over finite fields", Francesco PAPPALARDI (Università Roma Tre, Italie)
Cours 4: "Constructing elliptic curves over finite fields with prescribed order", Peter STEVENHAGEN (Leiden Universiteit, Pays-Bas)
Cours 5: "Heights and the Mordell-Weil theorem", Valerio TALAMANCA (Università Roma Tre, Italie)
Cours 6: "The Birch and Swinnerton-Dyer conjecture", René SCHOOF (Università di Roma "Tor Vergata", Italie)
Cours 7: "Elliptic curves algorithms, factoring and cryptography", Laura GEATTI (Università di Roma "Tor Vergata", Italie)
Cours 8: "Galois representations and L-series", Fernando RODRIGUEZ VILLEGAS (ICTP, Italie)
Site internet de l'école
Comment participer
Pour s'inscrire et candidater à un financement CIMPA, suivre les instructions données ici.
Date limite d'inscription et de candidature : 28 octobre 2018.