## Discrete Structures: Alegbra, Combinatorics and Geometry

07 Nov 2019, by Sponsored events in1st January 2020

Mathematics and Statistics, University of Lancaster, UK

A structure (consisting of revolute joints linked by stiff bars, and modelled by a graph) is rigid if the configuration space of all realisations with the given bar lengths consists only of isometries of the original structure. In dimensions 1 and 2 the generic behaviour of such structures is completely characterised by matroidal properties of the underlying graph and hence is amenable to efficient algorithms. These algorithms are used frequently in applications (for example by biophysicists and structural engineers), and extending them to 3-dimensions would be of great applied and theoretical importance.

This problem was known certainly by the 1920s and no widely believed conjecture even exists despite the analogous 2-dimensional statement being completely solved in the 1970s. The aim of this focussed research group is to gather experts from combinatorics and geometry with researchers from neighbouring geometric and algebraic fields, in order to make a coordinated attack on the problem.

**Organiser:**

Tony Nixon (Lancaster)

Further details can be found on the website closer to the time.