BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tony Nixon (Lancaster) DTSTART:20200507T140000Z DTEND:20200507T150000Z DTSTAMP:20260423T035636Z UID:VSAMRT/4 DESCRIPTION:Title: F lexible circuits and $d$-dimensional rigidity\nby Tony Nixon (Lancaste r) as part of Virtual seminar on algebraic matroids and rigidity theory\n\ n\nAbstract\nA framework is a geometric realisation of a graph in Euclidea n $d$-space. Edges of the graph correspond to bars of the framework and ve rtices correspond to joints with full rotational freedom. The framework is rigid if every edge-length-preserving continuous deformation of the verti ces arises from isometries of $d$-space. Generically\, rigidity is a rank condition on an associated rigidity matrix and hence is a property of the graph which can be described by the corresponding row matroid. Characteris ing which graphs are generically rigid is solved in dimension $1$ and $2$. However determining an analogous characterisation when $d\\geq 3$ is a lo ng standing open problem\, and the existence of non-rigid (i.e. flexible) circuits is a major contributing factor to why this problem is so difficul t. We begin a study of flexible circuits by characterising the flexible ci rcuits in $d$-dimensions which have at most $d+6$ vertices. This is joint work with Georg Grasegger\, Hakan Guler and Bill Jackson.\n LOCATION:https://researchseminars.org/talk/VSAMRT/4/ END:VEVENT END:VCALENDAR