A CIMPA research school on Elliptic Curves: Arithmetic and Computation Universidad de la República Montevideo, Uruguay February 11th - 22nd, 2019

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Schedule* * Small last minute adjustments are still possible Week 1 Monday Tuesday Wednesday Thursday Friday 09.00-09.50 Registration & Opening Ceremony Algebraic curves Christophe Ritzenthaler Algebraic curves Christophe Ritzenthaler Elliptic curves Elisa Lorenzo Garcia The Weak Mordell-Weil theorem Fernando Rodriguez Villegas 10.00-10.50 10.50-11.10 BREAK 11.10-12.00 Algebraic curves Christophe Ritzenthaler Elliptic curves Elisa Lorenzo Garcia Elliptic curves Elisa Lorenzo Garcia Diophantine equations and elliptic curves Fernando Rodriguez Villegas Elliptic curves over Local fields René Schoof 12.10-13.00 13.00-15.00 LUNCH 15.00-15.50 Galois cohomology Fernando Rodriguez Villegas     Complex elliptic curves     Peter Stevenhagen Free Afternoon Elliptic curves over finite fields Peter Stevenhagen Explicit 2-descent Peter Stevenhagen 16.00-16.50 Week 2 Monday Tuesday Wednesday Thursday Friday 09.00-09.50 Modular forms and elliptic curves Gonzalo Tornaria The Mordell-Weil Theorem Valerio Talamanca Modular forms and elliptic curves Gonzalo Tornaria Canonical heights Valerio Talamanca Elliptic curves algorithms Laura Geatti 10.00-10.50 10.50-11.10 BREAK 11.10-12.00 Heights on projrctive spaces Valerio Talamanca Elliptic curves algorithms Laura Geatti L-functions Francesco Pappalardi Elliptic curves algorithms Laura Geatti The Birch&Swinnerton-Dyer conjecture René Schoof 12.10-13.00 13.00-15.00 LUNCH 15.00-15.50 Computations with GP/PARI Francesco Pappalardi Computations with GP/PARI Francesco Pappalardi Free Afternoon Image of Galois René Schoof Modular forms and elliptic curves Gonzalo Tornaria 16.00-16.50 16.50-17.20 Merienda Merienda 17.20-19.00 Exercises session Exercises session