Following the pioneering work of Wilson who realized the phase space of the (classical complex) Calogero-Moser system as a quiver variety, Chalykh and Silantyev observed in 2017 that various generalizations of this integrable system can be constructed on quiver varieties associated with cyclic quivers. Building on these results, I will explain how such systems can be visualized at the level of quivers, and how to prove that we can form (degenerately) integrable systems. I will then outline how this construction can be adapted to obtain generalizations of the Ruijsenaars-Schneider system if one uses multiplicative quiver varieties associated with the same quivers. The main tool that I want to advertise is the notion of double (quasi-) Poisson brackets due to Van den Bergh. This talk is partly based on previous works with Oleg Chalykh and Tamás Görbe.
De Alexander Soibelman
De Mingkun Liu
De Anna Barbieri
De Gabriele Rembado
De Pierrick Bousseau
De Joshua Lam
De Oscar Kivinen
De Elba Garcia-Failde
