BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joel Fine (Université Libre de Bruxelles) DTSTART:20220315T163000Z DTEND:20220315T173000Z DTSTAMP:20260423T022627Z UID:Geolis/77 DESCRIPTION:Title: Knots\, minimal surfaces and J-holomorphic curves\nby Joel Fine (Unive rsité Libre de Bruxelles) as part of Geometria em Lisboa (IST)\n\n\nAbstr act\nLet K be a knot in the 3-sphere. I will explain how one can count min imal discs in hyperbolic 4-space which have ideal boundary equal to K\, an d in this way obtain a knot invariant. In other words the number of minima l discs depends only on the isotopy class of the knot. I think it should a ctually be possible to define a family of link invariants\, counting minim al surfaces filling links\, but at this stage this is still just a conject ure. “Counting minimal surfaces” needs to be interpreted carefully her e\, similar to how Gromov-Witten invariants “count” J-holomorphic curv es. Indeed I will explain how these counts of minimal discs can be seen as Gromov-Witten invariants for the twistor space of hyperbolic 4-space. Whi lst Gromov-Witten theory suggests the overall strategy for defining the mi nimal surface link-invariant\, there are significant differences in how to actually implement it. This is because the geometry of both hyperbolic sp ace and its twistor space become singular at infinity. As a consequence\, the PDEs involved (both the minimal surface equation and J-holomorphic cur ve equation) are degenerate rather than elliptic at the boundary. I will t ry and explain how to overcome these complications.\n LOCATION:https://researchseminars.org/talk/Geolis/77/ END:VEVENT END:VCALENDAR