Langlands Program
The Langlands Program is a research agenda that predicts deep connections between many areas of mathematics that might seem, on first glance, to be unrelated: number theory, representation theory, algebraic geometry and harmonic analysis to name a few. For this reason, the Langlands Program is sometimes described as the grand unified theory of mathematics. But in spite of its broad scope, the open problems in the Langlands Program are very specific and generally very precisely articulated. Although the Langlands Program is only fifty years old, amazing progress has already been made, especially in the last ten years, including a proof of the Fundamental Lemma and the local Langlands Correspondence for general linear, symplectic and special orthogonal groups, relying on the theory of endoscopy. Much work remains to be done, however, including a better understanding of the Langlands Correspondence for non-classical groups and the principle of functoriality especially beyond endoscopy. Results from the Langlands Program have applications in number theory and physics. My current research in the Langlands Program focuses on three projects: the Voganish Project; automorphic representations of GSpin attached to Abelian varieties; and geometrization of various parts of the Langlands Correspondence. Information about these projects and my small army of collaborators may be found at automorphic.ca.