Some topics related to Lie groupoids and quantization

The idea of this talk is to review some links between quantization and the Lie theory of symplectic groupoids. As well known, the product structure for quantum observables has the graph of a (local or formal) symplectic groupoid multiplication as its 'semiclassical shadow'. We shall put these ingredients in the light of new perspectives and explicit constructions within Lie theory that were developed in recent years. In particular, we will discuss the relation between: Kontsevich tree expansions, symplectic realizations and local groupoid generating functions (joint with B. Dherin; I. Marcut and M.A. Salazar); integrability of Poisson structures, non-formal quantizations and strong associativity of the quantum product (in progress, joint with R.L. Fernandes); the relation to field theoretic descriptions involving the Poisson Sigma Model (in progress).