The Hitchin system is an integrable system depending on a choice of a smooth complex Riemann surface and a positive integer. It was introduced by Nigel Hitchin in 1987. It received a huge amount of attention, partly because many classically known integrable systems can be embedded into the Hitchin system, partly because the system is related to many areas of mathematics such as algebraic geometry, Langlands program, and mathematical physics.
The main idea behind the Hitchin systems is a surprisingly simple linear algebra statement. I will explain this idea and define the Hitchin systems. Then I will formulate the Langlands duality for the Hitchin systems. Finally, I will discuss recent advances in this area as well as some new directions.
704 Thackeray Hall