Probability Seminar: Global well-posedness of the stochastic Abelian-Higgs equations in two dimensions

There has been much recent progress on the local solution theory for geometric singular SPDEs. However, the global theory is still open in most cases. My talk will be about global well-posedness for the 2D stochastic Abelian-Higgs model, which is a geometric singular SPDE arising from gauge theory. The proof is based on a new covariant (i.e. geometric) approach, which consists of two parts: (1) introducing covariant stochastic objects (2) controlling nonlinear remainders using a covariant monotonicity formula, which is inspired by earlier work of Hamilton.