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Derivation of kinetic wave equations: Feynman graphs and their combinatorics

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FKTW01 - Kinetic Theory: old and new tutorial

Kinetic wave equations provide a kinetic description of nonlinear dispersive equations in the weakly turbulent regime. I will first give an overview of this theory, which developed very rapidly over the last few years: what are its aims, and how far did we get? Then, I will introduce the mathematical tools needed to derive rigorously kinetic wave equations. The basic idea is to expand the solution in its data, to represent this expansion through Feynman graphs, and finally to use the graph structure to evaluate the contribution of the various terms.

This talk is part of the Isaac Newton Institute Seminar Series series.

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