Elliptic Curves: Arithmetic and Computation
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.