Unstable vector bundles on projective spaces

Speaker: Morgan Opie - UCLA

Abstract: In this talk, I will talk about the subtleties of studying unstable complex vector bundles on complex projective spaces using stable homotopy theory. I’ll start with a classical example of techniques used by Atiyah-Rees to classify all complex rank $2$ topological vector bundles on $\mathbb{C}P^5$ using real K theory and discuss my work on complex rank $3$ topological vector bundles on $\mathbb{C}P^5$ using topological modular forms. As time allows, I will talk about some new work involving the detection of higher rank bundles using other chromatic theories.