CMSA Geometry and Mathematical Physics Seminar: Nonlinear Schrödinger and Korteweg–de Vries from 4d Chern–Simons theory

Over the past decade, four-dimensional Chern–Simons theory has emerged as a powerful organising principle for two-dimensional integrability. In this talk, I will directly recover the Lax formulations and variational principles of two archetypal integrable systems within this framework: the nonlinear Schrödinger and Korteweg–de Vries equations. The key ingredients are singular boundary conditions supplemented by compensating source terms, in a construction reminiscent of oper boundary conditions in three-dimensional Chern–Simons theory.