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Elliptic Curves: Arithmetic and Computation


Montevideo, Uruguay


11/02/2019 to 22/02/2019


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. 

Administrative and scientific coordinators

Gonzalo TORNARÍA (Universidad de la República, Uruguay, tornaria@cmat.edu.uy )
Christophe RITZENTHALER (University Rennes 1 , France, christophe.ritzenthaler@univ-rennes1.fr )

Scientific committee

Laura GEATTI (Università di Roma "Tor Vergata", Italy)
Elisa LORENZO GARCIA (University Rennes 1, France)
Christophe RITZENTHALER (University Rennes 1, France)
René SCHOOF (Università di Roma “Tor Vergata” , Italy)
Talamanca VALERIO (Università Roma Tre, Italy)
Gonzalo TORNARIA (Universidad de la República, Uruguay)

Scientific program

Course 1: "Introduction to algebraic curves ", Elisa LORENZO GARCIA (University Rennes 1, France)
Course 2: "Elliptic curves", Christophe RITZENTHALER (University Rennes 1, France)
Course 3: "Elliptic curves over finite fields", Francesco PAPPALARDI (Università Roma Roma Tre, Italy)
Course 4: "Constructing elliptic curves over finite fields with prescribed order", Peter STEVENHAGEN (Leiden Universiteit, The Netherlands)
Course 5: "Heights and the Mordell-Weil theorem", Valerio TALAMANCA (Università Roma Tre, Italy)
Course 6: "The Birch and Swinnerton-Dyer conjecture", René SCHOOF (Università di Roma "Tor Vergata", Italy)
Course 7: "Elliptic curves algorithms, factoring and cryptography", Laura GEATTI (Università di Roma "Tor Vergata", Italy)
Course 8: "Galois representations and L-series", Fernando RODRIGUEZ VILLEGAS (ICTP, Italy)

Website of the school


How to participate:

For registration and application to a CIMPA financial support, follow the instructions given here

Deadline for registration and application:  October 28, 2018.