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SUMMARY:Geometric function theory and vortex motion: the role of connectio
 ns - Björn Gustafsson (KTH - Royal Institute of Technology )
DTSTART:20190912T090000Z
DTEND:20190912T100000Z
UID:TALK129448@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We discuss point vortex dynamics on a closed two-dimensional R
 iemann manifolds from the point of view of affine and other connections.  
 The speed of a vortex then comes out as the difference between two affine 
 connections\, one derived from the coordinate Robin function and the other
  being the Levi-Civita connection associated to the Riemannian metric.  &n
 bsp\;<br><br>  In a&nbsp\; Hamiltonian formulation of the vortex dynamics\
 , the Hamiltonian function consists of two main terms. One of them is a qu
 adratic form based on a matrix whose entries are Green and Robin functions
 \, while the other describes the energy contribution from those circulatin
 g flows besides those which are implicit in the Green functions.  These tw
 o terms are not independent of each other\, and one major issue is trying 
 to understand the exchange of energy between them.
LOCATION:Seminar Room 1\, Newton Institute
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