The geometric Langlands program can be described in a natural way by
compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills
theory in four dimensions. The key ingredients are electric-magnetic duality of
gauge theory, mirror symmetry of sigma-models, branes, Wilson and 't Hooft
operators, and topological field theory. Seemingly esoteric notions of the
geometric Langlands program, such as Hecke eigensheaves and D-modules, arise
naturally from the physics.Comment: 225 pp; further clarification
