Advances in Combinatorial and Geometric Rigidity (15w5114)


(Cornell University)

(Harvard University)

Tibor Jordan (Eotvos University, Budapest)

Brigitte Servatius (Worcester Polytechnic Institute)

(University of Florida)

(York University)


The Banff International Research Station will host the "Advances in Combinatorial and Geometric Rigidity" workshop from July 12th to July 17th, 2015.


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 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
behavior of natural structures such as proteins and nano-materials. 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 model 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, with even wider application in areas of computer aided design and manufacturing, CAD/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).