Gan-Gross-Prasad conjecture and its application in number theory

Gan-Gross-Prasad conjecture is one of the major conjectures in the area of automorphic forms, relating period integrals to L-values. In this talk, we will introduce this conjecture and survey its progress, mainly in the hermitian case, which has been fully solved. Then we will discuss its four applications in the Beilinson-Bloch-Kato conjecture, Iwasawa's main conjecture, subconvex bounds of L-values, and nonvanishing of L-values.