Quantization of symplectic grupoid and multiplicative integrable models

IMPA, November 4, 2019


Francesco Bonechi


13-14:30 and 15-16:30




I will present a class of non trivial examples where Weinstein's dream of quantizing Poisson manifolds through the quantization of the symplectic groupoid can be concretely realized.  The construction uses singular polarizations, for instance those given by integrable models that are
compatible with the groupoid structure. We call such models multiplicative. The main source of examples comes from Poisson-Nijenhuis geometry. In the first lecture I will discuss the quantization of the Bruhat-Poisson structure on complex projective spaces. In the second lecture I will discuss the Poisson-Nijenhuis structure defined on hermitian symmetric spaces.