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Explore a 49-minute lecture by Yu Deng that addresses a major component of the Hilbert sixth problem: deriving macroscopic equations of motion and kinetic equations from microscopic first principles. Learn about recent collaborative work with Zaher Hani and Xiao Ma examining both the hard sphere model in particle settings and the cubic nonlinear Schrödinger equation in wave settings. Discover how they derive corresponding kinetic equations for as long as solutions to these equations exist, representing a significant advancement toward resolving the Hilbert sixth problem. The talk connects classical Boltzmann kinetic theory, where the Boltzmann equation is derived from Newtonian dynamics, with wave turbulence theory, where wave kinetic equations emerge from nonlinear dispersive equations. This December 2024 presentation from the Simons Foundation's Collaboration on Wave Turbulence Annual Meeting offers valuable insights into mathematical physics and differential equations.
