Kelvin's Topological Vortex Dynamics - Lecture 1

Explore the foundations of topological vortex dynamics in this advanced lecture, the first of a five-part series delivered at the Institut d'Études Scientifiques de Cargèse. Delve into key concepts such as velocity fields, Biosavar, kinetic energy, Kelvin circulation, and Faraday's equation. Examine the intricacies of vortex motion, including vortex lines and tubes, and their behavior in fluid dynamics. Investigate the Jacobian matrix, deformation processes, and the fascinating concept of fluid knots. Gain a comprehensive understanding of these complex topics through this in-depth, nearly two-hour lecture designed for advanced students and researchers in the field.