Geometric Rigidity Workshop

The underlying graph of a 3-dimensional isostatic framework. (Courtesy of Derek Kitson) The underlying graph of a 3-dimensional isostatic framework. (Courtesy of Derek Kitson)

A Geometric Rigidity One Day Workshop was organised by Derek Kitson with support from the EPSRC project "Crystal frameworks, operator theory and combinatorics".

On the 5th June we had seven presentations ranging over fundamental results in a diverse spread of geometric rigidity topics and some collaborations continued over the following day.

Bill Jackson (Queen Mary, University of London) and John Owen (Siemens) informed us of their beautiful definitive characterisation of rigid 2D "point-line frameworks". This generalises Laman's classical theorem to frameworks which incorporate angle data in place of some distance data. The solution leads to implementable computer-aided design algorithms that are variants of the "pebble game".

Bill's second talk outlined joint work with Tibor Jordan (Budapest) and Shin-ichi Tanigawa (Kyoto) that brings geometric rigidity techniques to attack the low rank matrix completion problem (of relevance in Machine Learning). Oleg Karpenkov (Liverpool) amazed us with the intricate stratification (fibre-wise) of the configuration space of K5 in 2D.

James Cruickshank (Galway) gave us insights into the longstanding Graver-Tay-Whiteley conjecture and Derek Kitson (Lancaster) presented new graph theoretic and combinatorial challenges which arise in his project with Bernd Schulze (Lancaster) on the rigidity of symmetric bar-joint frameworks in non-Euclidean spaces. Finally, Stephen Power (Lancaster) spoke about two developing Lancaster projects, namely the almost periodic rigidity for crystal frameworks (with Derek and Ghada Badri), and the notion of mean flexibility dimension for quasicrystal frameworks (with Bernd and Derek).

Tue 17 June 2014