About quantization and symplectic groupoids

Abstract: In this talk, we will review some recent topics relating quantization of Poisson manifolds and (local) symplectic groupoids. In particular, focusing on the case of a Poisson structure on a coordinate domain, we will explain how analytic Lie-theoretic formulas are related to a ("tree level") part of Kontsevich's star product formula after a suitable Taylor expansion. We will also comment on the relation to the Poisson Sigma Model through a system of PDEs that captures its semiclassical contributions. If time permits, we will also briefly comment on how the integrability into a global symplectic groupoid is reflected on quantizations.

mathematical physicsdifferential geometryquantum algebrasymplectic geometry

Audience: researchers in the topic

Deformation Quantization Seminar