QQ-systems and tropical geometry
The QQ systems are systems of polynomial equations that arise in various geometric settings, including the enumerative geometry of Nakajima varieties and elements of the (deformed) geometric Langlands correspondence. These equations are related to the integrable models of spin chain type, linked to quantum groups and Yangians. Specifically, the solutions to the QQ-system equations characterize the spectrum of these integrable models via the so-called Bethe ansatz equations.