Higher presentation theory

I will study the higher representation theory of affine Lie algebras both in its geometric and its algebraic aspects. I will apply the techniques to construct invariants of three- and four-dimensional manifolds. The research stems from the modern idea that much can be learned by categorifying familiar mathematical objects; the structure becomes much richer and sheds light on old, classical problems. I will add to the Australian community in this thriving field and make progress on the major current problems in algebra and low-dimensional topology.