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UID:6368@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210622T110000
DTEND;TZID=Europe/Paris:20210622T120000
DTSTAMP:20241120T201413Z
URL:https://www.i2m.univ-amu.fr/evenements/knots-minimal-surfaces-and-j-ho
 lomorphic-curves/
SUMMARY:Joel Fine (Université Libre de Bruxelles): Knots\, minimal surface
 s and J-holomorphic curves
DESCRIPTION:Joel Fine: I will describe work in progress\, parts of which ar
 e joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I wil
 l explain how one can count minimal surfaces in hyperbolic 4-space which h
 ave ideal boundary equal to L\, and in this way obtain a knot invariant. I
 n other words the number of minimal surfaces doesn’t depend on the isoto
 py class of the link. These counts of minimal surfaces can be organised in
 to a two-variable polynomial which is perhaps a known polynomial invariant
  of the link\, such as HOMFLYPT.\n \n“Counting minimal surfaces” need
 s to be interpreted carefully here\, similar to how Gromov-Witten invarian
 ts “count” J-holomorphic curves. Indeed I will explain how this “min
 imal surface polynomial" can be seen as a Gromov-Witten invariant for the 
 twistor space of hyperbolic 4-space. This leads naturally to a new class o
 f infinite-volume 6-dimensional symplectic manifolds with well behaved cou
 nts of J-holomorphic curves. This gives more potential knot invariants\, f
 or knots in 3-manifolds other than the 3-sphere. It also enables the count
 ing of minimal surfaces in more general Riemannian 4-manifolds\, besides h
 yperbolic space. \n\n\nParticiper à la réunion Zoom\nhttps://univ-amu-f
 r.zoom.us/j/91572513888?pwd=dituMDVkWGtpK256Wk5xa1ZqQ3ZNQT09\n \nID de r
 éunion : 915 7251 3888\nCode secret : voir mail\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Joel_Fine.jpg
CATEGORIES:Séminaire,Géométrie Complexe,Virtual event
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