Z/2-equivariant orthogonal calculus

This project lies within homotopy theory: the study of topological spaces up to continuous deformations. Here a topological space is a mathematical notion of shape, one that includes familiar objects such as circles, spheres and Klein bottles; their higher dimensional analogues and many more abstract objects. The idea of orthogonal calculus is that some of these topological spaces can be filtered by linear subspaces of Euclidean spaces. One should think of having a shape for each line in the plane, that can be combined into a shape corresponding to said plane. Then we repeat the process for each plane in three-dimensional space and so on. In this project will be including symmetries into this filtration, in order to better study spaces with symmetries, specifically those with a bilateral symmetry (a single line or plane of reflection).

This project fits into EPSRCs strategy of "supporting strong leadership within the community of researchers working in geometry and topology, to ensure that existing excellence is preserved in the longer term and that the UK continues to have specialist capabilities to lead the global research landscape"

The methodology will be based around extending current results on linear subspaces of Euclidean spaces to include these symmetries, relating the approach to recent work on a related notion of equivariant functor calculus and the supervisor's expertise in equivariance and model structures.