AbstractThe theory of wave turbulence is the statistical theory of interacting waves, or the wave analog of Boltzmann's kinetic theory. It started in the works of Peierls in the 1920s, and has had substantial developments in the 20th century, with significant applications in science. The mathematical study of this subject started with the early works of Spohn and Erdös-Yau et al. on linear mode...
AbstractThis course will cover the geometric foundations of metaverse technologies, including the main concepts and theorems in algebraic topology, differential geometry, Riemann surface theory and optimal transportation theory. Then the computational methods for persistent homology, conformal parameterization, mesh generation, surface Ricci flow and the optimal transportation maps will be intr...