Hilbert's Sixth Problem - From Particles to Waves

Explore a groundbreaking mathematical lecture that addresses one of the most significant unsolved problems in mathematical physics. Learn about recent breakthrough work that extends Lanford's 1975 theorem to long times, finally enabling the full execution of Hilbert's program for deriving fluid mechanics equations from kinetic theory. Discover how the Boltzmann-Grad limit connects particle systems to wave phenomena, and understand the mathematical foundations underlying the transition from microscopic particle behavior to macroscopic fluid dynamics. Examine the innovative strategies developed through collaborative research that resolved parallel problems in wave turbulence theory, where colliding particles are replaced by nonlinear waves. Gain insights into the rigorous mathematical framework that bridges Boltzmann's kinetic theory with the Euler and Navier-Stokes equations of fluid mechanics. Follow the historical development from Hilbert's original formulation through mid-20th century contributions by Grad and Cercignani, to the recent advances that solve this decades-old challenge. Understand the implications for both pure mathematics and mathematical physics, particularly in establishing the theoretical foundations of wave turbulence theory and fluid dynamics.