URegina Topology and Geometry Seminar: Yang Hu

Pick your favorite manifold $M$and a positive integer $r$: how many $r$rank (topological) complex vector bundles are there over $M$up to isomorphism? While the question is accessible via K-theory in the stable range, unstably such bundles become much harder to compute and to detect.

In this talk, we will demonstrate how the orthogonal/unitary calculus of Weiss — a version of functor calculi — can be applied to study unstable topological vector bundles. We will present several counting results for complex vector bundles over ${\mathbb{CP}}^n$in the metastable range, and, time permitting, introduce an equivariant version of the theory along with some potential applications in equivariant geometry. This talk contains joint work with Hood Chatham and Morgan Opie, and with Prasit Bhattacharya.