BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Charlotte Aten (University of Rochester) DTSTART:20220125T200000Z DTEND:20220125T210000Z DTSTAMP:20260423T004728Z UID:PALS/23 DESCRIPTION:Title: Or ientable smooth manifolds are essentially quasigroups\nby Charlotte At en (University of Rochester) as part of PALS Panglobal Algebra and Logic S eminar\n\n\nAbstract\nIn my recent work with Semin Yoo we produced a gener alization of a construction of Herman and Pakianathan which assigns to eac h finite noncommutative group a closed surface in a functorial manner. We give a pair of functors whose domain is a subcategory of a variety of n-ar y quasigroups. The first of these functors assigns to each such quasigroup a smooth\, flat Riemannian manifold while the second assigns to each quas igroup a topological manifold which is a subspace of the metric completion of the aforementioned Riemannian manifold. I will give examples of these constructions\, draw some pictures\, and argue that all homeomorphism clas ses of smooth orientable manifolds arise from this construction. I will th en discuss a connection with the Evans Conjecture on partial Latin squares \, give its implication for orientable surfaces\, and state a related prob lem applicable to our construction for compact n-manifolds.\n LOCATION:https://researchseminars.org/talk/PALS/23/ END:VEVENT END:VCALENDAR