Equivariant Orthogonal Calculus

Current research project

The primary focus of my research is on functor calculus. In particular orthogonal homotopy calculus, which is the study of functors from the category of finite dimensional real vector spaces to the category of pointed topological spaces. Such functors are of great interest, as they arise naturally within algebraic topology. We can construct a Taylor tower of approximations (a similar idea to a Postnikov tower) to such functors, consisting of polynomial functors. The benefit of this theory is that the layers of this tower are characterised by spectra with O(n) action, which are much better understood than spaces.

I aim to extend the theory of orthogonal calculus to an equivariant setting, in which the layers of the tower have symmetries on them. I will then use the tools provided by model categories of stable equivariant homotopy theory to study these layers.

Biography

Presently, I am undertaking my first year of PhD research at QUB. I graduated in June 2020 with an MSci degree in Mathematics at QUB. My undergraduate dissertation project focussed on the theory of Manifolds and Lie Groups, and solidified my interest in algebraic topology.

Research interests

• Homotopy Theory

• Functor Calculus