Title：Compatible Poisson structures on multiplicative quiver varieties
Reporter：Maxime Fairon
Work Unit：Université de Bourgogne
Time：Feb.29 20:00-22:00
Address：ZOOM Id：904 645 6677，Password：2024
Link: https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=87511211646
Summary of the report:
Any multiplicative quiver variety is endowed with a Poisson structure constructed by M. Van den Bergh through reduction from a Hamiltonian quasi-Poisson structure. The smooth locus of this variety carries a corresponding symplectic form defined by D. Yamakama through quasi-Hamiltonian reduction. In this talk, I want to explain how to include this Poisson structure as part of a larger pencil of compatible Poisson structures on the multiplicative quiver variety. The pencil is defined by reduction from a pencil of (non-degenerate) Hamiltonian quasi-Poisson structures, whose construction can be adapted to various frameworks, e.g. in relation to character varieties. I will start by explaining the simpler analogous situation that leads to a pencil of Poisson structures on (additive) quiver varieties, before detailing the multiplicative case. Moreover, I will show that it is possible to understand the construction through the lens of non-commutative Poisson geometry. Time allowing, I may comment on the application of this result to the spin Ruijsenaars-Schneider phase space; this shows the compatibility of two Poisson structures that appeared in independent works of Arutyunov-Olivucci (arXiv:1906.02619) and of Chalykh and myself (arXiv:1811.08727).
Introduction of the Reporter:
Maxime Fairon is Maître de Conférences (equivalent to lecturer) at Institut de Mathématiques de Bourgogne, Université de Bourgogne, Dijon, France. His research interests are split between: i) classical integrable systems appearing in mathematical physics, and ii) non-commutative Poisson geometry.
