BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joel Fine DTSTART:20220503T140000Z DTEND:20220503T150000Z DTSTAMP:20260423T052834Z UID:Freemath/78 DESCRIPTION:Title: Knots\, minimal surfaces and J-holomorphic curves\nby Joel Fine as p art of Free Mathematics Seminar\n\n\nAbstract\nLet K be a knot or link in the 3-sphere\, thought of as the ideal boundary of hyperbolic 4-space\, H^ 4. The main theme of my talk is that it should be possible to count minima l surfaces in H^4 which fill K and obtain a link invariant. In other words \, the count doesn’t change under isotopies of K. When one counts minima l disks\, this is a theorem. Unfortunately there is currently a gap in the proof for more complicated surfaces. I will explain “morally” why the result should be true and how I intend to fill the gap. In fact\, this (c urrently conjectural) invariant is a kind of Gromov—Witten invariant\, c ounting J-holomorphic curves in a certain symplectic 6-manifold diffeomorp hic to S^2xH^4. The symplectic structure becomes singular at infinity\, in directions transverse to the S^2 fibres. These singularities mean that bo th the Fredholm and compactness theories have fundamentally new features\, which I will describe. Finally\, there is a whole class of infinite-volum e symplectic 6-manifolds which have singularities modelled on the above si tuation. I will explain how it should be possible to count J-holomorphic c urves in these manifolds too\, and obtain invariants for links in other 3- manifolds.\n LOCATION:https://researchseminars.org/talk/Freemath/78/ END:VEVENT END:VCALENDAR