Thoughts on Regularity Structures

Explore Felix Otto's insights on regularity structures in this 53-minute lecture from the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into Hairer's framework for solving partial differential equations driven by extremely rough noise, requiring renormalization of nonlinearities. Discover the versatility of concepts like structure groups and modelled distributions, extending beyond traditional combinatorics of decorated trees and diagrams. Learn how these tools align with a more analytic approach, incorporating derivatives with respect to nonlinearity-defining constitutive laws and noise (Malliavin derivative). Gain a deeper understanding of this powerful mathematical framework and its applications in solving complex differential equations.