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. In this presentation, I will outline how tropical geometry techniques have been effectively applied to find solutions to these equations. I will provide a detailed explanation of how these methods function for QQ-systems, focusing on the XXX/XXZ Heisenberg spin chain and the associated Gaudin model. This is a joint work with Anton Zeitlin.
Thackeray 427