Tony Nixon: Rigidity of Graphs on Expanding Spheres

We consider the rigidity of graphs realised on concentric d-spheres in d+1 dimensions where the radii of the spheres are allowed to vary independently. To do this we use coloured graphs and realisations of these graphs where vertices with the same colour correspond to spheres whose radii vary at the same rate. For d=1 with arbitrary number of colours and for d=2 with at most 3 colours we provide characterisations of generic rigidity in terms of count functions on these coloured graphs.

The lecture was held within the framework of the Hausdorff
Trimester Program: Combinatorial Optimization.