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Explore advanced mathematical concepts in this conference talk examining regularity properties for invariant measures of singular stochastic partial differential equations (SPDEs). Delve into the resolution of a longstanding question regarding the equivalence between the invariant measure for stochastic 2D Navier-Stokes equations and Gaussian measures. Learn about the fine properties of random fields and their applications spanning from fluid dynamics to quantum field theory. Gain insights into cutting-edge research in stochastic nonlinear systems, including well-posedness, dynamics, and numerical methods. Discover how modern mathematical techniques are applied to understand complex random phenomena in both classical fluid mechanics and quantum theoretical frameworks. This presentation was recorded during the thematic meeting "New trends of stochastic nonlinear systems: well-posedeness, dynamics and numerics" at the Centre International de Rencontres Mathématiques in Marseille, France, providing access to world-class mathematical research and methodology in the field of stochastic analysis.
