Explore the intricacies of singularity formation in nonlinear dispersive partial differential equations in this 44-minute lecture presented by Galina Perelman for the International Mathematical Union. Delve into advanced mathematical concepts and gain insights into the behavior of complex systems governed by these equations. Examine the conditions and mechanisms that lead to the development of singularities, and understand their implications for various physical phenomena. Enhance your understanding of mathematical analysis and its applications in studying wave propagation, fluid dynamics, and other related fields.