My main research interests are in Geometric Rigidity Theory, which  can be traced back to classical work of Euler, Cauchy and Maxwell on the rigidity of polyhedra and skeletal frames. Both the generic combinatorial theory and symmetric geometric theories are  active research areas. Recent excitement has  come from new themes such as constraint systems with  symmetries, constraint systems in general normed linear spaces, infinite geometric structures, and from emerging connections with other mathematical areas, such as matrix completion theory and machine learning.

I am happy to supervise PhD projects in these areas, as are other members of the Geometric Rigidity group at Lancaster.

Geometric rigidity, infinite bond-node structures, crystallographic and quasicrystallographic bar-joint frameworks, rigidity operators, rigid unit modes, locally compact graphs and string-node meshes.

 Finite and infinite bar-joint frameworks

 Functional Analysis

 Operator Algebras, Limit Algebras, Operator Theory

http://www.maths.lancs.ac.uk/~power/