Rachel Ollivier - Columbia University - Elementary introduction to the Langlands correspondence - December 10, 2012

The Langlands program, initiated in the 1960s, is a set of conjectures predicting a unification of number theory and representation theory of groups. This program is based on the Langlands correspondence which is a way to interpret results in number theory in terms of group theory, and vice versa. Through elementary examples, we will illustrate this correspondence and suggest why it can be seen as a non abelian reciprocity law. At the end, we will try to sketch some open questions and directions in this area.