BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marcy Robertson (University of Melbourne) DTSTART:20201026T203000Z DTEND:20201026T213000Z DTSTAMP:20260423T004914Z UID:MITTop/16 DESCRIPTION:Title: Expansions\, completions and automorphisms of welded tangled foams\nby Marcy Robertson (University of Melbourne) as part of MIT topology seminar \n\n\nAbstract\nWelded tangles are knotted surfaces in $\\mathbb{R}^4$. Ba r-Natan and Dancso described a class of welded tangles which have “foame d vertices” where one allows surfaces to merge and split. The resulting welded tangled foams carry an algebraic structure\, similar to the planar algebras of Jones\, called a circuit algebra. In joint work with Dancso an d Halacheva we provide a one-to-one correspondence between circuit algebra s and a form of rigid tensor category called ``wheeled props.'' This is a higher dimensional version of the well-known algebraic classification of p lanar algebras as certain pivotal categories.\n\n\nThis classification all ows us to connect these ``welded tangled foams\,'' to the Kashiwara-Vergne conjecture in Lie theory. In work in progress\, we show that the group of homotopy automorphisms of the (rational completion of) the wheeled prop o f welded foams is isomorphic to the group of symmetries KV\, which acts on the solutions to the Kashiwara-Vergne conjecture. Moreover\, we explain\n how this approach illuminates the close relationship between the group KV and the pro-unipotent Grothendieck--Teichmüller group.\n LOCATION:https://researchseminars.org/talk/MITTop/16/ END:VEVENT END:VCALENDAR