Associative half-densities and quantization

Talk by Dr. Alejandro Cabrera

Date: 30.03.26  Time: 13.30 - 14.30  Room: Y27H25

In this talk, the idea is to first motivate the appearance of half-densities along the graph of a symplectic groupoid multiplication as a semiclassical approximation to a star product. Then, we introduce the corresponding associativity axiom and present an existence and classification result for such structures. Finally, we apply this theory to understand structurally the "1-loop factor" in Kontsevich's star product for a coordinate Poisson manifold. We also discuss in detail the case of a linear Poisson structure in which "Duflo factors" appear naturally as an underlying canonical half-density. This is based on joint work with G. Ledesma.