Singular Vortex Configurations and Coadjoint Orbits

Explore singular vortex configurations and coadjoint orbits in this 56-minute lecture from the Workshop on Geometry and Analysis of Fluid Flows, presented by Cornelia Vizman from West University of Timisoara. Delve into classes of coadjoint orbits of the area preserving diffeomorphism group of R2 that accommodate singular vorticities for ideal 2D fluids. Examine vortex loops, pointed vortex loops, and vortex loops with dipoles. Investigate how certain coadjoint orbits emerge through symplectic reduction in dual pairs, including the Marsden-Weinstein ideal fluid dual pair and a new variant of the Holm-Marsden EPDiff dual pair. Gain insights into the geometric and analytical aspects of fluid flows in this specialized mathematics lecture.