Lectures on the Langlands Program and Conformal Field Theory

Abstract

These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric reformulation, addressed primarily to physicists. I tried to make it as self-contained as possible, requiring very little mathematical background. Next, we describe the connections between the Langlands Program and two-dimensional conformal field theory that have been found in the last few years. These connections give us important insights into the physical implications of the Langlands duality.

Based on the lectures given by the author at the Les Houches School "Number Theory and Physics" in March of 2003 and at the DARPA Workshop "Langlands Program and Physics" at the Institute for Advanced Study in March of 2004