BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Patrick Lin (University of Illinois at Urbana-Champaign) DTSTART:20200702T140000Z DTEND:20200702T150000Z DTSTAMP:20260423T052624Z UID:VSAMRT/9 DESCRIPTION:Title: M axwell-Cremona meets the flat torus\nby Patrick Lin (University of Ill inois at Urbana-Champaign) as part of Virtual seminar on algebraic matroid s and rigidity theory\n\n\nAbstract\nWe consider three classes of geodesic embeddings of graphs on the plane and the Euclidean flat torus: graphs ha ving a positive equilibrium stress\, reciprocal graphs (for which there is an orthogonal embedding of the dual graph)\, and weighted Delaunay comple xes. The classical Maxwell-Cremona correspondence and the well-known corre spondence between convex hulls and weighted Delaunay triangulations imply that these three concepts are essentially equivalent for plane graphs. How ever\, this three-way equivalence does not extend directly to geodesic gra phs on the torus. Reciprocal and Delaunay graphs are equivalent\, and ever y reciprocal graph is in positive equilibrium\, but not every positive equ ilibrium graph is reciprocal. We establish a weaker correspondence: Every positive equilibrium graph on any flat torus is equivalent to a reciprocal /Delaunay graph on some flat torus. These results appeared in SoCG '20\n LOCATION:https://researchseminars.org/talk/VSAMRT/9/ END:VEVENT END:VCALENDAR