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Rigidity and flexibility of periodic frameworks: Recent progress and open questions

Banff International Research Station for Mathematical Innovation and Discovery

Rigidity Theory is concerned with the rigidity and flexibility analysis of bar-joint frameworks and related constraint systems of geometric objects. This area has a rich history which can be traced back to classical work of Euler, Cauchy and Maxwell on the rigidity of polyhedra and skeletal frames. In the first part of this talk I will give an introduction to the theory of local and global rigidity of bar-joint frameworks and related structures such as body-bar and body-hinge frameworks, and provide an overview of the key results. In the second part of the talk I will discuss the recent progress on extending these results to infinite periodic frameworks. I will also discuss some key open questions in this area, some of which have potential applications in crystallography, materials science and condensed matter physics.

Mathematics; Convex and discrete geometry; Statistical mechanics, structure of matter; Discrete mathematics

video/mp4

Author affiliation: Lancaster University

2021-01-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/77127

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/