Equisingularity of Real Mappings

This project concerns Singularity Theory - a branch of mathematics invented by Isaac Newton when he invented calculus.In some sense the purpose of this research is simple. I wish to take a collection of objects and decide whether the objects are alike. An everyday example could be that the collection of objects is a group of school children and I will say that the two children are alike if they are the same age.If all the elements of the family are alike, then we say that the family is equisingular. In a more mathematical setting I am interested in collections of surfaces, (but I can also work with really weird objects that live in higher dimensions). I want to take some measurements from each surface in the collection and from those measurements decide whether all the surfaces are alike. In other words I am looking for what are the important defining features.In the example of the group of school children there is an obvious measurement to make: ask each one their age!The techniques developed in this project can later be used in other subjects such as computer vision.