The Hitchin equations are an integrable system in two-dimensions that plays a variety of important roles across mathematics and physics and this talk will start with some of this motivation.  It will go on to discuss how the 4d Chern-Simons of Costello, Witten and Yamazaki fits into ideas from  30-40 years ago that sought to unify the study of integrable systems via the study of the self-duality equations and their twistor constructions.  In particular 4d Chern-Simons provides a uniform approach to 2d integrable systems and their canonical structures.  The Hitchin equations have been missing in this approach and this talk will explain I will explain how Hitchin equations are incorporated with reductions to Toda and Sine Gordon, and  gives new approaches to understanding canonical strucures associated with these equations.  This talk is based on joint work with Roland Bittleston and Faroogh Moosavian https://arxiv.org/abs/2601.05309.

 Hydrodynamics provides a universal low-energy effective description of interacting many-body systems. Traditionally, it is formulated in terms of equations of motion derived from the relevant conservation laws. However, this classical framework neglects fluctuations of hydrodynamic observables required by the fluctuation–dissipation theorem (FDT). The Schwinger–Keldysh effective field theory (SK EFT) offers a Wilsonian, action-based formulation of hydrodynamics that systematically incorporates such fluctuations. In this approach, the effective action is generically non-unitary (complex), encoding macroscopic dissipation, while the FDT is implemented through a discrete Kubo–Martin–Schwinger (KMS) symmetry. This symmetry also underlies the emergence of the second law of thermodynamics within hydrodynamics.