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Delve into the second lecture of a four-part graduate-level series on super critical singularities in non-linear partial differential equations. Explore the fascinating world of front singularities and their formation in defocusing problems, with a particular emphasis on their connections to fluid mechanics. Gain insights into recent discoveries and advancements in the field, building upon the classical understanding of bubbling phenomena in focusing problems. Learn about key results, open problems, and essential proof techniques as presented by Pierre Raphaël from the University of Cambridge. This two-hour lecture offers a comprehensive introduction to this complex topic, suitable for graduate students and researchers interested in the intersection of mathematics and physics.
