This is a graduate course, not a general lecture. While all are welcome to attend, please keep in mind that the core audience of these courses is a cohort of students taking them for credit and being evaluated by course leaders, in part, on their participation.

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This course will survey various aspects of inviscid fluid flows with concentrated vorticity in two dimensions, where there is a reasonably complete theory, as well as three dimensions, where many basic questions remain open. It will address both classical and quantum mechanical fluids. The behavior of concentrated vortices touches on many areas of mathematics and will be approached with a wide range of mathematical tools and perspectives, including formal asymptotic analysis, nonlinear elliptic PDE and the calculus of variations, symplectic geometry, geometric measure theory, nonlinear dispersive equations, and both classical and modern aspects of fluid dynamics proper. The course will be accessible to graduate students with a basic knowledge of PDEs and real analysis.

Speakers Notes:

Sept 9-14 (pdf file)

Sept 16 (pdf file)

Sept 21 (pdf file)

Sept 23 (pdf file)

Sept 24 (pdf file)