The Langlands program is a vast generalization of classical reciprocity laws such as the law of quadratic reciprocity. One of the key aspects of the program is the principle of functoriality which predicts relations between spectra of arithmetic manifolds arising from different algebraic groups. When the arithmetic manifolds are actually algebraic varieties, it is natural to ask whether functoriality is given by an algebraic cycle (or correspondence). I will give some examples and then describe some recent work in this direction.
Speaker(s): Kartik Prasanna (University of Michigan)