Arithmetic Gross-Prasad conjecture for unitary Shimura varieties

This proposal is to support the work of the Wei Zhang who propose to work on several projects on arithmetic algebraic geometry, in particular, automorphic forms and Shimura varieties. In particular to prove the refined Gross-Prasad conjecture for unitary groups in three variables using the relative trace formulae of Jacquet-Rallis secondly to prove a Gross-Zagier type formula for unitary Shimura varieties using the approach of the arithmetic relative trace formulae initiated by W.Zhang recently,and thirdly to study their applications to the Beilinson-Bloch conjecture and Bloch-Kato conjecture on the relation between Chow groups, Selmer groups and L-values.

This proposal will provide support for a recent PhD, now a PostDoc at Harvard to pursue research in Number Theory and Representation Theory. This research concerns a special type of function known as an L-function which encodes information about geometry and arithmetic.