Morgan Opie: Vector bundles on projective spaces

Abstract

Given the ubiquity of vector bundles, it is perhaps surprising that there are so many open questions about them -- even on projective spaces. In this talk, I will outline my ongoing work on complex rank 3 topological vector bundles on \(\mathbb{CP}^5\). In particular, I will describe a classification of such bundles which involves a surprising connection to topological modular forms; a concrete, rank-preserving additive structure which allows for the construction of new rank 3 bundles on \(\mathbb{CP}^5\) from "simple" ones; and future directions related to this project.

Zoom Notes: The meeting ID is 657 9019 8929 and the passcode is 3517257.