Holomorphic-topological theories: gauge theory applied to integrability

In recent years, a novel approach to studying integrable models has emerged which leverages a higher-dimensional gauge theory, specifically a holomorphic-topological theory. This new framework provides alternative methods for investigating quantum aspects of integrability and for constructing integrable models in more than two dimensions. This talk will review the foundations of this approach, its applications, and the exciting possibilities it opens up for future research in the field of integrable systems.