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This lecture, the first in a series of four, explores the complex dynamics of nonlinear dispersive waves presented by Professor Daniel Tataru from UC Berkeley at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the fundamental properties of linear dispersive flows, where waves with different frequencies travel at varying group velocities, leading to dispersive decay. Examine how nonlinear dispersive flows enable interactions between linear waves, and understand how their long-term behavior is determined by the balance between linear dispersion and nonlinear effects. Discover a new set of conjectures aimed at describing global well-posedness and dispersive properties of solutions in challenging scenarios where nonlinear effects dominate, even with small initial data. Learn about recent breakthroughs in this field through Professor Tataru's collaborative work with Mihaela Ifrim from the University of Wisconsin, Madison. This two-hour scientific presentation is available on CARMIN.tv, a French video platform specializing in mathematics and interdisciplinary research.
