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Geometric Langlands From Six Dimensions
Edward Witten
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-di…
Geometric Langlands And The Equations Of Nahm And Bogomolny
Edward Witten
Geometric Langlands duality relates a representation of a simple Lie group to the cohomology of a certain moduli space associated with the dual group . In this correspo…
Branes, Instantons, And Taub-NUT Spaces
Edward Witten
ALE and Taub-NUT (or ALF) hyper-Kahler four-manifolds can be naturally constructed as hyper-Kahler quotients. In the ALE case, this construction has long been understood in terms o…
The Problem Of Gauge Theory
Edward Witten
I sketch what it is supposed to mean to quantize gauge theory, and how this can be made more concrete in perturbation theory and also by starting with a finite-dimensional lattice…