# Faculty Area Research (FARS)

## Location

Our speaker this week is Ravi Vakil.

**Title**: The space of vector bundles on spheres: algebra, geometry, topology**Abstract:** Bott periodicity relates vector bundles on a topological space X to vector bundles on X \times S^2: the “moduli space” BU of complex vector bundles is basically the same as the “moduli space” maps of a sphere to BU. I’m not a topologist, so I will try to explain an algebraic or geometric incarnation, in terms of vector bundles on the Riemann sphere. The algebro-geometric incarnation of Bott periodicity is actually motivated by important current questions in geometry. I will attempt to make the talk introductory, and (for the most part) accessible to those in all fields, at the expense of speaking informally. (These are things I am thinking about with Hannah Larson, and separately, with Jim Bryan.)