Affiliation:
Princeton University
Date:
Thu, 12/06/2014 - 10:00 - 11:00
In his eccentrically written paper in 1952, Heegner showed that the 1000 years old congruent number problem is soluble for all prime $p$ (or $2p$) congruent to 5, 7 (or 6) mod 8, by constructing some rational points on certain elliptic curves of infinite order. In 1986, Gross and Zagier proved a formula which relates the heights of Heegner points and derivatives of $L$-series. At the ICM in 1986, Faltings asked: "Alles in allem handelt es sich um eine schöne Entdeckung, welche wir aber leider noch nicht "erklären" können: Warum ist sie richtig?"