Integrable systems and Seiberg-Witten geometry 

The Seiberg-Witten solution for the low energy limit of N=2 supersymmetric field theories relies on the deep geometry of the Coulomb branch (Described by me here: • The Seiberg-Witten sol... . In this talk I dive deeper, interpreting the Coulomb branch geometry as a variation of Hodge structure. This POV reveals the somewhat mysterious role of the seiberg-witten differential, which turns the variation of Hodge structure into an integrable system! This is a sort of "unified approach" to BPS states, trying together the seiberg-witten perspective and its stringy origin. (Mathematically, this equivalence equates a Hitchin system with a Calabi-Yau integrable system)