Rigidity Theory: Progress, Applications and Key Open Problems (12w5069)


(Cornell University)

Tibor Jordan (Eotvos University, Budapest)

(University of Lancaster)

(Smith College)

(York University)


The Banff International Research Station will host the "Rigidity Theory: Progress, Applications and Key Open Problems" workshop from July 15th to July 20th, 2012.

The rigidity and flexibility of a structure, either man-made in buildings, linkages, and lightweight deployable forms, or found in nature ranging from crystals to proteins, is critical to to the form, function, and stability of the structure. The mathematical theory of `rigidity and flexibility' is developing methods for the analysis and design of man-made structures, as well as predictions of the behaviour of natural structures such as proteins. The shared methods can help predict when a drug will alter the function of a protein (changing its flexibility), when a robot arm can move an object into location, and when a novel material in a computer design will have stable physical properties when built.

We live in 3-dimensions, and a fundamental problem is to develop results for 3-dimensions which are as good, and as efficient, as the recently developed theory for structures in 2-dimensions. These problems have been identified for over 150 years, and major progress has been made in the last two decades. However, critical problems remain and possible extensions continue to be identified. The mathematical methods also give insights into fundamental mathematical systems of constraints and computations for these, with even wider application in areas design with CAD and in manufacturing with CAM.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).