No matter what discoveries are made at the Large Hadron Collider in Switzerland when it begins operating next year, its a sure thing that gauge fields (i.e., connections on vector bundles) will continue to play the central role in elementary particle theory that they have for the past 40 years. The quantization of a pure gauge field amounts, informally, to the construction of a suitable measure on the configuration space of the gauge field, (i.e., the moduli space: connection forms modulo gauge transformations.) This is an infinite dimensional manifold which must be chosen large enough, in some distribution sense, to support this measure. In this talk I am going to show how one can hope to realize such nonlinear distribution spaces as spaces of geometric flows. Specifically, I will describe the state of the art for the Yang-Mills heat equation on a three manifold with boundary.