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## Rigidity theory and the concept of global rigidity

### Brigitte Servatius

Worcester Polytechnic Institute

###
Thursday, April 13, 2006

L01 Carson Hall, 4 pm

Tea 3:30 pm, Math Lounge

**Abstract: ** 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.
We will describe combinatorial tools for planar rigidity, in
particular the new characterization of global rigidity, and discuss
algorithmic questions as well as problems arising in the attempts to
generalize these results from the plane to 3-space.

This talk will be accessible to undergraduates.