Vendredi 14 Octobre
Heure: 
10:30  12:00 
Lieu: 
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13 
Résumé: 
Géométrie Arithmétique et Motivique  Supersingular main conjectures, Sylvester's conjecture and Goldfeld's conjecture  
Description: 
Daniel KrizI will present a rank 0 and 1 pconverse theorem for CM elliptic curves defined over the rationals in the case where p is ramified in the CM field. This theorem has applications to two classical problems of arithmetic: it verifies Sylvester's conjecture on primes expressible as a sum of two rational cubes and establishes Goldfeld's conjecture for the congruent number family. The proof relies on formulating and proving a new Iwasawa main conjecture, which in turn involves new methods arising from interplays between Iwasawatheoretic objects and relative padic Hodge theory on the infinitelevel Shimura curve. 

