Algebra/Topology Seminar 14122020

Speaker: Morgan Opie

Title: 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 some results about vector bundles on projective spaces, including my ongoing work on complex rank 3 topological vector bundles on CP^5. In particular, I will describe a classification of such bundles which involves a connection to topological modular forms; a concrete, rank-preserving additive structure which allows for the construction of new rank 3 bundles on CP^5 from simple ones; and, as time allows, future directions related to this project.