Langlands Correspondence for Loop Groups

The Langlands Program was conceived initially as a bridge between Number Theory and Automorphic Representations, and has now expanded into such areas as Geometry and Quantum Field Theory, weaving together seemingly unrelated disciplines into a web of tantalizing conjectures. This book provides a new chapter in this grand project. It develops the geometric Langlands Correspondence for Loop Groups, a new approach from a unique perspective offered by affine Kac-Moody algebras.
The theory offers fresh insights into the world of Langlands dualities, with many applications to Representation Theory of Infinite-dimensional Algebras and Quantum Field Theory. This introductory text builds the theory from scratch, with all necessary concepts defined and all essential results proved along the way.

Based on courses taught by the author at Berkeley, the book provides many open problems which could form the basis for future research, and is accessible to advanced undergraduate students and beginning graduate students.