Speaker:  Bob Connelly, Cornell
Title:   Global Rigidity.
Time: 2:30 PM, Monday, September 7, 2009
Place:  Malott 206

Abstract:  Consider a straight line embedding of a finite graph in Euclidean space.  When any other embedding of the graph is congruent to the original, we say it is globally rigid.  How do you tell?  Recent results of Jordán, Jackson, and Berg have provided a good answer in terms of combinatorial conditions on the graph for the Euclidean plane when the configuration is of vertices of the graph are in generic position.   More recently Gortler, Healey, and Thurston have shown that a numerical criterion, in terms of a stress matrix that I showed was sufficient, was also necessary again in the generic case.  Even more recently, Jordán, Whiteley and I have shown that when the graph is composed of rigid bodies joined by bars, then there is polynomial-time combinatorial algorithm that computes its generic global rigidiy.  I also will present a general conjecture that implies that a large class of graphs are generically globally rigid and in these cases provides a configuration that can be checked for global rigidity without appealing to the configuration being generic.

October 1, 2009