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The importance of roles played by the Quantized Vortices in superfluids (or vorticies in classical fluids which may not Necessarily be quantized) can never be over stated. The studies of these such subjects have attracted a great attentions to many theoretical physists as well as mathematicians. They provide numerous fascinating and difficult mathematical problems. My talk is to explain some background and a couple mathematical problems that I have personally involved over the last 20 years.
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