Timothy F. Havel - The role of tensegrity in distance geometry

Distance geometry is an invariant-theoretic approach to Euclidean (and classical non-Euclidean) geometry, which was developed in large part by A. Cayley, K. Menger, I. J. Schoenberg, J. J. Seidel, and L. M. Blumenthal. This approach has proved useful in mathematical studies of the kinematics of mechanisms, and in numerical studies of the conformations of molecules. Tensegrity frameworks are an architectural novelty introduced by K. Snelson and popularized by B. Fuller, whose constructions and mathematical properties have been extensively studied by R. Connelly and colleagues. A key result has been an algebraic criterion which can identify tensegrity frameworks that are globally rigid, meaning that all realizations of the framework are congruent. This talk will describe the insights that Connelly's results have brought to the applications of distance geometry to molecular conformation, and conversely, some new insights which the perspective of distance geometry brings to the theory of tensegrity frameworks.