When he heard of the progress being made with the fundamental lemma, whose proof was provided by Ngô Bảo Châu in 2010,  Robert Langlands began working in an area he calls “beyond endoscopy.” Primary among Langlands’s interests is using the Arthur-Selberg trace formula to resolve the principle of functoriality beyond endoscopy. “I hope that with the fundamental lemma at hand," said Langlands, "we will see in the coming years great progress both with functoriality and with the general theory of Shimura varieties.”