Langlands program consists of a collection of
surprising conjectures which relate algebraic geometry, algebraic number
theory, harmonic analysis, and representation theory. On the other hand,
Quantum Field Theory (and Gauge Theory) is the best existing framework of
physics which describes our universe on the micro scale. In recent years there
have been surprising applications of QFT to Geometric Langlands Program, the
geometric version of Langlands program.
In this course, we will learn the mathematical
ingredients composing the Geometric Langlands Program. At the same time, we
will also learn the physical ingredients that make sense of supersymmetric
gauge theories mathematically and find their relations to the original program,
partially following the influential work of Kapustin and Witten. Towards the
end, we will discuss some applications of the physics perspective that lead to
new mathematical results.