Geometric Langlands Program and Dualities in Quantum Physics
Abstract
The Langlands Program was conceived initially as a bridge between Number Theory and Automorphic Representations, but it has now expanded into such areas as Geometry and Quantum Field Theory. Remarkably and surprisingly, the same salient features, such as the Langlands dual group, appear in these different contexts. Understanding the hidden patterns of the Langlands duality may thus hold the key to many important problems in modern mathematics and physics. One of the most exciting developments in this area in the last few years has been the work of Edward Witten and collaborators unifying the Langlands Program with dualities in quantum field theory and string theory. Specifically, they have related the so-called S-duality of the four-dimensional gauge theory to the geometric Langlands correspondence via the dimensional reduction from four to two dimensions. My work on this project continued this line of research as well as other topics on Langlands duality in Representation Theory, Geometry and Quantum Physics.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 30, 2009
- Accession Number
- ADA519424
Entities
People
- Edward Frenkel
Organizations
- University of California, Berkeley