Singular vortex dynamics and nonlinear Schrodinger equations

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Physical and numerical experiments reveal an unexpected dynamical behaviour of vortex filaments in ideal fluids and superfluids. This unexpected behaviour manifests itself in the appearance of singular shapes, such as corners, in the evolution of the vortex. The proposed research aims to advance our mathematical understanding of the processes leading to formation of such singularities in some well-known models for the evolution of vortex filaments, and in certain intimately related nonlinear Schr\"odinger equations.