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Personal profile

Research Interests

Homotopy theory, functor calculus, and related fields. 

 

My personal webpage with more information may be found here: https://sites.google.com/view/nialltaggartmath

Research Focus

My research interests lie in algebraic topology, where one uses tools from algebra to study properties (invariants) of topological spaces. I am particularly interested in stable homotopy theory with an equivariant flavour, 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 from functors from the category of complex vector spaces to the category of topological spaces and analysing the homotopy theory of such a calculus. I am also interested in how the various versions of functor calculi relate to each other. 

I am also interested in more general questions. For example, the Blakers-Massey Theorem for cubes is a well-established result relating the connectivity of homotopy limits and colimits. Together with collaborators, I am trying 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.

Teaching

I am currently a teaching assistant on PMA3017 Metric and Normed Spaces.

In previous years I have been a teaching assistant on PMA1020 Numbers, Vector and Matrices, PMA2002 Analysis, and PMA2008 Group Theory. 

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Prizes

Burgess Prize

Niall Taggart (Recipient), Jul 2017

Prize: Prize (including medals and awards)