Servatius, Brigitte; matematični kolokvij maj 2003

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Rigidity Theory and its Applications

Brigitte Servatius

Worcester Polytechnic Institute, ZDA, in Univerza v Ljubljani

22. maj 2003

A framework is a mathematical model of a physical structure: Each vertex of the framework corresponds to a ball joint located in space, the edges correspond to rigid rods connecting the joints. A very general class of physical structures, from scaffolding or bridges to glasses, ceramics, or molecules of proteins, may be described this way. The mathematical task is to develop a method for predicting rigidity without building a model. Geometry and combinatorics provide the fundamental tools. Although rigidity has been studied since the time of Maxwell (1864), it is only in the last 25 years that it has begun to find applications in the basic sciences. Concentrating on the combinatorial aspects of the theory, we will describe the major results of the last decade and their applications to CAD, statistical physics, and biochemistry.

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