Mike Hopkins (University of Harvard, USA)

Homotopy theory and algebraic vector bundles

Abstract:  This talk will describe joint work with Aravind Asok and Jean Fasel using the methods of homotopy theory to construct new examples of algebraic vector bundles.   I will describe a natural conjecture which, if true, implies that over the complex numbers the classification of algebraic vector bundles over smooth affine varieties admitting an algebraic cell decomposition coincides with the classification of topological complex vector bundles.