18th October: Martin Ortiz

Title: Langlands as non-abelian class field theory: an example

Abstract: There are different ways of thinking about Langlands reciprocity, but not all come at the same level of sophistication. In this talk I will explain how elementary questions such as the quadratic reciprocity law, and the pursuit of higher reciprocity laws fit in the modern formulation of the Langlands program. In a way class field theory gives reciprocity laws for polynomials whose splitting field is abelian, and the Langlands reciprocity would be a way to access all the nonabelian ones, although not much is known in this regard. As an example I will explicitly construct the case of cubic reciprocity.