Elliptic Curves: Arithmetic and Computation

Emplacement

MONTEVIDEO
,
Uruguay

Dates

à

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

Gonzalo TORNARÍA (Universidad de la República,
Uruguay
, )
Christophe RITZENTHALER (Université Rennes 1 ,
France
, )

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.