In 2015, Chalykh and Silantyev observed that generalisations of the classical Calogero-Moser system with different types of spin variables can be constructed on quiver varieties associated with cyclic quivers. Building on their work, I will explain how such systems can be visualised at the level of the quiver, and how to prove that we can form (degenerately) integrable systems. I will then outline how this construction can be adapted to obtain generalisations of the Ruijsenaars-Schneider system if one uses multiplicative quiver varieties associated with the same quivers. The main tool used in these constructions is a version of noncommutative Poisson geometry due to Van den Bergh, which I will briefly sketch. Time allowing, I will say how to derive the elliptic Calogero-Moser system in a similar way by going beyond the quiver case. This talk is based on previous works with O. Chalykh (Leeds) and T. Görbe (Groningen), and an ongoing work with O. Chalykh.  

https://indico.math.cnrs.fr/event/8971/