The goal of this proposal is to investigate the functoriality principle in the function field case. The starting points are Langlands' paper 'Beyond Endoscopy', Beilinson and Drinfeld's conjecture and the recent proof of the Fundamental Lemma to which the PI contributed in a crucial way. Strong ties among these elements will provide a new road to general functoriality in the function field case and will give direction to further investigation in the number field case as well.
Building on the PI's recent success in proving certain cases of the Fundamental Lemma, a central question in the Langlands program, the research program in this award offers a new set of deep and exciting problems for young researchers in the domain of algebraic geometry and representation theory.
