# 2006 Bowen Lectures

*The Twenty-Sixth Annual Bowen Lectures were delivered by Edward Witten on November 13, 14, and 15.*

The Bowen lectures are supported by an anonymous donor, who was an undergraduate student of Professor Bowen.

Department of Mathematics, University of California, Berkeley, presents

The 2006 Bowen Lectures

Edward Witten

The Charles Simonyi Professor of Mathematical Physics

Institute for Advanced Study Princeton

(Photo at right provided by IAS.)

**Gauge Theory and the Geometric Langlands Program**

*Abstract:*These talks will discuss how electric-magnetic duality of four-dimensional gauge theory can be used to describe the geometric Langlands Program. The Associated two-dimensional picture is mirror symmetry of the moduli space of Higgs bundles. The 't Hooft operators of gauge theory become the geometric Hecke operators of the geometric Langlands program, and the basic statements about these operators come from electric-magnetic duality applied to Wilson and 't Hooft operators. Ramified flat bundles are incorporated by allowing impurities in the four-dimensional gauge theory that are supported on a submanifold of codimension two.

**Lecture I: Overview**

**Monday, November 13**

120 Latimer - 4:10pm-5:00pm

**Reception in 1015 Evans at 5:15 pm following Monday's lecture.**

**Lecture II: 't Hooft and Hecke Operators**

**Tuesday, November 14**

10 Evans - 4:10pm-5:00pm

**Lecture III: Gauge Theory and Ramification**

**Wednesday, November 15**

Sibley Auditorium, Bechtel Hall - 11:10am-12:00pm

**To download PDF files of the slides for these lectures, click on the corresponding link at the bottom of this page.**