Vector bundles over unordered configuration spaces

I will describe a recent construction of a symmetrized external tensor product of vector bundles of unordered configuration spaces (over some fixed manifold M). Together with the usual tensor product this construction induces a 2-monoidal structure on these vector bundles and naturally appears when trying to construct a geometric model for the multilocal observables in field theory. I will also discuss how equipping the configuration with a certain natural bornology can compensate the fact that they are non-compact, even when the initial manifold M is. This is based on joint work with Alessandra Frabetti and Olga Kravchenko