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Explore mathematically rigorous advances in wave turbulence theory through this 53-minute conference talk that examines both established and recent developments in the field. Begin with Bourgain's foundational approach to studying energy spectra in periodic nonlinear Schrödinger equations through Sobolev norm growth analysis. Progress to understanding wave kinetic equations as effective models for energy spectrum behavior, and examine concrete examples of rigorously proven condensate growth and energy transfer phenomena. Gain insights into collaborative research findings developed with N. Camps and B. M. Tran that contribute to the mathematical understanding of wave turbulence dynamics and energy distribution mechanisms.
