Quantum field theory (QFT) originated in physics in the context of
elementary particles. Although, over the years, surprising and profound
connections to very diverse branches of mathematics have been discovered,
QFT does not have, as yet, found a universally accepted "standard"
mathematical formulation. In this talk, I shall outline an approach to QFT
that emphasizes its underlying algebraic structure. Concretely, this is
represented by a concept called "Operator Product Expansion". I explain the
properties of such expansions, how they can be constructed in concrete QFT
models, and the emergent relationship between "perturbation theory" on the
physics side and
"Hochschild cohomology" on the physics side. This talk is based on joint
work
with Ch. Kopper and J. Holland from Ecole Polytechnique, Paris.