Morgan Opie, UCLA

Abstract: In this talk, I will outline my work on complex rank 3 topological vector bundles on CP^5. I will describe a classification of such bundles using twisted, topological modular form-valued invariants. This builds a parallel with Atiyah and Rees' classification of rank 2 topological vector bundles on CP^3, using real k-theory. I will also discuss methods for producing topological vector bundles of rank 3 on CP^5. As time allows, I will outline future directions, including: possible connections between higher real K-theories and vector bundles on projective spaces, and algebraic generalizations of my current work.