I am a student of both mathematics and physics, who has recently been studying string theory. My mathematics background is mostly differential geometry (principal bundles, Lie groups, etc.), although starting this semester I am planning to study algebraic geometry and Lie algebras (particularly infinite dimensional Lie algebras, such as current algebras). Now, in the long term, I am interested in studying the connections between $\mathcal N = (2,0)$ superconformal field theory and geometric Langlands as well as the connections between $S$-duality and the latter, as described in the following papers of Witten: Geometric Langlands From Six Dimensions and Electric-Magnetic Duality And The Geometric Langlands Program.
Now, let's suppose that someone has understood algebraic geometry at the level of Hartshorne, superstring theory at the level of Green, Schwarz, & Witten, and Lie algebras at the level of the book Current Algebras and Groups or Kac's Infinite Dimensional Lie Algebras. What then would be the best roadmap (of books, papers, etc.) to learn about the remaining prerequisites of the geometric Langlands correspondence? I am aware of the book Representation Theory and Complex Geometry by Ginzburg and Chriss for geometric representation theory, but after this, what should one use to study geometric Langlands? What prerequisites remain, and how should one best go about learning them?
