Maxime Fairon: Quivers and integrable systems

Salle 318 (IMB)

Salle 318 (IMB)


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.