BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jack Morava (Johns Hopkins University) DTSTART:20211110T230000Z DTEND:20211111T003000Z DTSTAMP:20260412T203117Z UID:SAGO/13 DESCRIPTION:Title: On the group completion of the Burau representation\nby Jack Morava (Joh ns Hopkins University) as part of Algebra Seminar (presented by SMRI)\n\n\ nAbstract\nOn fundamental groups\, the discriminant \\prod_{i \\neq k} (z_ i - z_k) \\in \\C^\\times of a finite collection of points of the plane de fines the abelianization homomorphism sending a braid to its number of ove rcrossings less undercrossings or writhe. In terms of diffeomorphisms of t he punctured plane\, it defines a kind of `invertible topological quantum field theory' associated to the Burau representation\, and in the classica l physics of point particles the real part of its logarithmic derivative i s the potential energy of a collection of Coulomb charges\, while its imag inary part is essentially the Nambu-Goto area of a loop of string in the t hree-sphere. \n \nIts higher homotopy theory defines a very interesting a double-loop map \n\\Z \\times \\Omega^2 S^3 \\to \\Pic(S^0)\nto the cate gory of lines over the stable homotopy ring-spectrum\, related to Hopkins and Mahowald's exotic (E_2) multiplication on classical integral homology\ , perhaps related to the `anyons' of nonclassical physics.\n\n(based on jo int work with D Rolfsen)\n LOCATION:https://researchseminars.org/talk/SAGO/13/ END:VEVENT END:VCALENDAR