The p-adic Gross-Zagier formula and Iwasawa theory of elliptic curves

After recalling the celebrated formula by Gross and Zagier relating the derivative of the Hasse-Weil L-function of elliptic curves to Heegner points, I explain its p-adic analog and an application for the Birch and Swinnerton-Dyer conjecture. I will also overview the Iwasawa theory of elliptic curves, which plays a crucial role in the application.