On a conjecture of Kurihara and its refinement

Motivated by considerations in the equivariant Iwasawa theory of elliptic curves, Kurihara formulated a nonvanishing conjecture for certain analytic quantities (modulo powers of p) constructed from modular symbols. The conjecture admits a natural refinement linked with the conjectural Birch-Swinnerton-Dyer formula. In this talk I will explain a proof of Kurihara's conjecture and its refinement (for primes p>2 of good reduction) obtained in joint work with Takamichi Sano.