Kinetic wave turbulence theory: full range of scaling laws

Yu Deng, University of Southern California
Fine Hall 314

We present recent work with Zaher Hani (Michigan) that establishes the wave kinetic approximation for nonlinear Schrödinger (NLS) equation, for the full range of scaling laws that quantify the large box and weak nonlinearity limits. This completes the program, initiated in our earlier works, of providing a rigorous mathematical foundation for the wave turbulence theory. The proof involves refined analysis of very high order Feynman diagrams, including a new robust combinatorial algorithm and delicate cancellations between highly complicated diagrams that are identified as the result of this new algorithm.