GT seminar: "Compatible Poisson structures on multiplicative quiver varieties"

Abstract: 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. This is based on arXiv:2310.18751.

This is a talk in our geometry and topology seminar series.