Niall Taggart

Current research project

Unitary Homotopy Calculus

My research interests lie in algebraic topology. I am particularly interested in stable homotopy theory, and the applications of such to functor calculus.

Functor calculus may be thought of as a version of Taylor's Theorem from differential calculus applied to functors satisfying particular properties. Current projects include constructing a variant of functor calculus for functors from the category of complex vector spaces to the category of topological spaces. I am also interested in how the various versions of functor calculi relate to each other.

The Blakers-Massey Theorem for cubes is a well-established result relating the connectivity of homotopy limits and colimits. I am working to extend this result to diagrams indexed on the poset of subspaces of the n-plane. This project is interesting in its own right but should also give valuable insight into analytic functors in orthogonal calculus, a rather unexplored class of functors, despite their important role in Goodwillie calculus.

Biography

I am currently a third year Ph.D. student at Queen’s University Belfast. Before starting my Ph.D., I completed an MSci degree in Mathematics at QUB, during which my project examined the interactions between group theory and topology. As an undergraduate I always had a flourish for topology, starting with analysis in first and second year, and leading to me winning the Burgees Prize for the best topology student in final year.

Research interests

• Homotopy theory

• Functor calculus and related fields

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