Pure Mathematics Seminar: James Cruickshank
James Cruickshank, NUI Galway
Wednesday 30 October 2013, 1500-1600
A54, Postgraduate Statistics Centre Lecture Theatre
Henneberg operations on three dimensional bar and joint frameworks
Bar and joint frameworks are a mathematical abstraction of structures made from rigid bars that are joined together with universal joints. A fundamental problem in this theory is to give necessary and sufficient conditions for such a framework to be rigid.
For frameworks in the plane this problem was solved by Laman in 1970 - at least for suitably generic frameworks. On the other hand the corresponding three dimensional problem remains, somewhat surprisingly perhaps, open.
A sticking point seems to be our lack of understanding of Henneberg operations in three dimensions - these are certain graph theoretic constructions that arise naturally in this context. In the talk we will survey the mathematical background to this problem, and describe some recent work which sheds some new light on the problem with Henneberg operations.