Singular Stochastic PDE: More Geometry and Less Combinatorics

Explore a 56-minute lecture on singular stochastic partial differential equations (PDEs) delivered by Felix Otto at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the concept of singular stochastic PDEs, where noise is so rough that nonlinearity requires renormalization. Examine the guiding principle of renormalization in preserving solution manifold symmetries. Follow the mathematical physics approach and Hairer's regularity structures for formal series expansion of general solutions. Discover a more geometric and analytic version of this approach, focusing on partial derivatives with respect to the "constitutive" function defining nonlinearity, rather than tree-indexed expansions. Learn about Malliavin derivatives and their role in characterizing expansion without divergent terms. Understand how this calculus, combined with spectral gap estimates, provides a natural path toward stochastic estimates. Gain insights into collaborative research efforts with P. Linares, M. Tempelmayr, P. Tsatsoulis, J. Sauer, S. Smith, and H. Weber in this advanced mathematical exploration.