Prof. Shouwu-Zhang, Columbia
"Gross-Schoen cycles, triple L-series, and effective Mordell"
In this talk I will explain some relations (proved or conjectuered)
among the following quantities for a curve of genus greater than
or equal to 3: the height of Gross-Schoen cycles, the central values or
derivatives of certain triple L-series, and the self intersection
of the relative dualising sheaf. A consequence of these relations
is an upper bound of the height of rational point when the
corresponding central value of L-series is non-vanishing.