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Explore recent advancements in the study of randomness propagation under dispersive PDE flow in this comprehensive lecture. Delve into a non-technical overview of two resolved open problems: Gibbs measure invariance for 2D NLS with arbitrary wave interactions and 3D cubic NLW. Discover the method of random averaging operators used to prove the first problem, and learn about the application of random tensor theory, paracontrolled calculus, and heat-wave analysis in solving the second. Gain insights from Andrea Nahmod of the University of Massachusetts as she presents collaborative work with Yu Deng, Haitian Yue, and Bjoern Bringmann, offering a deeper understanding of these complex mathematical concepts in the field of dispersive partial differential equations.
