BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Thomas Kindred DTSTART:20210426T190000Z DTEND:20210426T200000Z DTSTAMP:20260423T004820Z UID:mitgt/16 DESCRIPTION:Title: R eplumbing definite surfaces: the geometric content of the flyping theorem< /a>\nby Thomas Kindred as part of MIT Geometry and Topology Seminar\n\n\nA bstract\nIn 1898\, P.G. Tait asserted several properties of alternating li nk diagrams\, which remained unproven until the discovery of the Jones pol ynomial in 1985. By 1993\, the Jones polynomial had led to proofs of all o f Tait's conjectures\, but the geometric content of these new results rema ined mysterious.\n\nIn 2017\, Howie and Greene independently gave the firs t geometric characterizations of alternating links\; as a corollary\, Gree ne obtained the first purely geometric proof of part of Tait's conjectures . Recently\, I used these characterizations and "replumbing" moves\, among other techniques\, to give the first entirely geometric proof of Tait's f lyping conjecture\, first proven in 1993 by Menasco and Thistlethwaite.\n\ nI will describe these recent developments\, focusing in particular on the fundamentals of plumbing (also called Murasugi sum) and definite surfaces (which characterize alternating links a la Greene). As an aside\, I will use these two techniques to give a simple proof of the classical result of Murasugi and Crowell that the genus of an alternating knot equals half th e degree of its Alexander polynomial. The talk will be broadly accessible. Expect lots of pictures!\n LOCATION:https://researchseminars.org/talk/mitgt/16/ END:VEVENT END:VCALENDAR