Professor Liu Yifeng has online published a research paper by Annals of Mathematics

Isolation of cuspidal spectrum, with application to the Gan–Gross–Prasad conjecture


We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet–Rallis relative trace formula, we complete the proof of the global Gan–Gross–Prasad conjecture and its refinement Ichino–Ikeda conjecture for U(n)×U(n+1)U(n)×U(n+1) in the stable case.