摘要：In their 1986 paper, Gross and Zagier proved a formula relating a special rational point on an elliptic curve to the first derivatives of the L-function of that elliptic curve. The Gross-Zagier formula, when combining with Kolyvagin’s method of Euler system yields a major result towards the Birch–Swinnerton-Dyer conjecture for elliptic curves. Since then the problem of generalizing this fundamental result to higher dimensional algebraic varieties has attracted considerable attention. In this expository talk we will present some of the generalizations with relatively recent results and outline some of the remaining challenges, with an emphasis on Kudla’s program and the arithmetic Gan-Gross-Prasad conjecture. Similar to the Gross-Zagier formula, the high dimensional generalizations have found applications to the construction of special elements in Chow groups and to the Beilinson-Bloch-Kato conjecture. 

This talk aims for a general audience and no prior knowledge on the topic is required.