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SUMMARY:Reconnection\, vortex knots and the fourth dimension
DTSTART:20170530T141500
DTEND:20170530T153000
DTSTAMP:20260413T182932Z
UID:993583219bfcc26a19e9687e7447c573638db4e66e744bfb563080bd
CATEGORIES:Conferences - Seminars
DESCRIPTION:Louis Kauffman (University of Illinois at Chicago)\nVortex kno
 ts tend to unravel into collections of unlinked circles by writhe-preservi
 ng reconnections. We can model this unravelling by examining the world lin
 e of the knot\, viewing each reconnection as a saddle point transition. Th
 e world line is then seen as an oriented cobordism of the knot to a disjoi
 nt collection of circles. Cap each circle with a disk (for the mathematics
 ) and the world line becomes an oriented surface in four-space whose genus
  can be no more than one-half the number of recombinations. Now turn to kn
 ot theory between dimensions three and four and find that this genus can b
 e no less than one-half the Murasugi signature of the knot. Thus the numbe
 r of recombinations needed to unravel a vortex knot K is greater than or e
 qual to the signature of the knot K. This talk will review the backgrounds
  that make the above description intelligible and we will illustrate with 
 video of vortex knots and discuss other bounds related to the Rasmussen in
 variant. This talk is joint work with William Irvine.
LOCATION:MA 10
STATUS:CONFIRMED
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