Apply methods from topological data analysis to derive a new approach to quantifying the geometric symmetries of three-dimensional shapes. 

A range of projects are available applying and developing the tools of topological data analysis. Data include 2D and 3D digital images, structural motifs in molecular-dynamics simulations, porous materials and more. 

Explore the geometry and symmetries of surfaces and other mathematical objects and their relevance in physical, chemical and biological contexts. 

Periodic frameworks, viewed as simple mechanisms, can be rigid or display a variety of exotic deformation properties such as surface modes or expansive auxetic motion. This project will conduct a systematic search for frameworks with these properties.