Integrability from Chern Simons

Integrable models represent a unique domain of exploration where complex systems exhibit a remarkable level of order. This is typically expressed through an infinite number of symmetries, which in turn, allow for the construction of an infinite number of independently conserved charges. The existence of such a large number of conserved quantities imposes stringent constraints on the system, which may render it soluble to some extent; it is precisely this solvable character what makes integrable systems so special. In recent years, significant progress has been made in the study of integrable systems from a gauge theoretic perspective. This development originated with the introduction of 4d Chern-Simons theory with defects, which provided a systematic framework for constructing two-dimensional integrable systems. In this talk we will introduce what makes integrable systems so special and explain how many of the special properties of such systems are captured using Chern-Simons theories in higher dimensions.