Geometry in orbital integrals and beyond

The Gross-Zagier formula is an identity between the first derivative of the L-function of an elliptic curve at s=1 and an intersection number. In joint work with Wei Zhang, we give a generalization of the Gross-Zagier formula to higher derivatives of the L-function for elliptic curves over function fields. In this series of lectures, I will discuss some geometric ideas involved in the proof of this formula which originated from the study of orbital integrals.

This is the first talk in a series. See http://www-personal.umich.edu/~bhattb/spring-lectures/springl-2017.html for more. Speaker(s): Zhiwei Yun (Yale University)