Explore the Heisenberg homology of surface configurations in this 49-minute lecture by Christian Blanchet, presented at the Workshop on Quantum symmetries: Tensor Categories, Topological quantum field theories, Vertex algebras. Delve into the Heisenberg group of a surface, defined as the central extension of its one-dimensional homology associated with the intersection cocycle. Discover how a representation of the Heisenberg group defines local coefficients on the unordered configuration space of points in the surface. Examine the corresponding homologies, Mapping Class Group actions, and their connection to quantum constructions. Learn about the collaborative research behind these findings, involving work with Awais Shaukat, Martin Palmer, and ongoing projects with Anna Beliakova, Jules Martel, and Marco de Renzi.