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Edge waves on the boundary of vortex matter

Mathematics Colloquium

Edge waves on the boundary of vortex matter
Series: Mathematics Colloquium
Location: MATH 501
Presenter: Paul (Pavel) Wiegmann, University of Chicago

Vortex matter is a dense uniform liquid assembly of same sense vortices in  incompressible two-dimensional flow, a turbulent flows with sign-like eddies.   I discuss two novel phenomena (i) a boundary layer of vorticity (vorticity layer), and (ii) a nonlinear wave propagating  within the vorticity layer, the edge wave. Both are lost if  the vortex matter  is approximated as a continuous  vorticity patch. The edge wave is governed  by the integrable Benjamin-Davis-Ono equation exhibiting solitons with a quantized total vorticity and identified  with the action of the Virasoro-Bott group, the centrally extended   diffeomorphisms of the circle. The boundary wave is a hydrodynamic analog of the edge states of the fractional quantum Hall effect. 

(Refreshments will be served in the Math Commons Room at 3:30 PM)