Niall Taggart  Student Profile
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 BlakersMassey Theorem for cubes is a wellestablished 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 nplane. 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 Queenâ€™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