Energy Lagrangian flows for singular SPDEs and applications

Energy Lagrangian flows are an extension of the Lagrangian flows of Di Perna-Lions and their stochastic counterparts by Le Bris-Lions and Figalli to the setting of singular SPDEs, partly in regimes where classical and pathwise theories break down. A key notion is "probabilistic subcriticality": even for scaling critical or supercritical equations, regularity of the law combined with coercivity of the generator may yield existence and uniqueness. I will outline the construction and well-posedness results, the relation to pathwise constructions, and applications to quantitative convergence theorems. Based on joint works with Ana Djurdjevac, Lukas Gräfner, and Shyam Popat.