One of the most fundamental descriptions of shape and structure is via topology - the mathematical description of how many connected components, independent loops and enclosed voids an object has. Topological Data Analysis uses this fundamental viewpoint to extract signatures of shape from many different types of data, from point clouds to digital images, pairwise distance matrices, and even text documents. This information can give insight into many different problems.
Recent work in this area from my group includes
Current and upcoming projects include
Projects range from data analysis to physical modelling to mathematical derivation of results and will be tailored to suit interested students with physics or mathematics background.