Universal Ambient Spaces, Quantum Field Theory, and General Relativity

In this video, we touch the bleeding edge of modern mathematics (using fibered algebroids and measured quantum groupoids) to reconstruct quantum field theory as a theory of coends that instantiate non-commutative geometries within a global Hilbert space, and then we quickly construct an adjoint theory of ends to express the commutative geometry of general relativity. Lastly, we show how their relationship allows us to consider theories of quantum gravity.