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The gradient flow of O'Hara's knot energies

Presented by: 
S Blatt University of Warwick
Date: 
Thursday 6th December 2012 - 11:45 to 12:05
Venue: 
INI Seminar Room 1
Session Title: 
Knots in mathematics: Tight Knots, etc.
Session Chair: 
Rob Kusner
Abstract: 
All of us know how hard it can be to decide whether the cable spaghetti lying in front of us is really knotted or whether the knot vanishes into thin air after pushing and pulling at the right strings.

In this talk we approach this problem using gradient flows of a family of energies introduced by O'Hara in 1991-1994.We will see that this allows us to transform any closed curve into a special set of representatives - the stationary points of these energies - without changing the type of knot. We prove longtime existence and smooth convergence to stationary points for these evolution equations.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons