|XXXVIII Workshop on Geometric Methods in Physics||30.06-6.07.2019|
|VIII School on Geometry and Physics||24-28.06.2019|
Participants of Workshop
Participants of School
Quiver varieties and integrable systems
I will first review the formalism of double Poisson and quasi-Poisson brackets, due to Van den Bergh. This provides a method for performing (quasi-)Hamiltonian reduction leading to quiver varieties (going back to Nakajima) and their multiplicative version (due to Crawley-Boevey and Shaw). The (multiplicative) quiver varieties thus form a rich class of Poisson varieties, and it is natural to ask whether they accommodate interesting integrable systems. I will explain how the classical Calogero--Moser system and its variants can be produced starting from fairly simple quivers. Based on joint works with A. Silantyev (Dubna) and M. Fairon (Leeds).
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