Mathematics Seminar Series: Topology

To what extent do Chow-valued Chern classes determine the isomorphism class of an algebraic vector bundle? When restricted to a smooth affine variety, this question is accessible via motivic obstruction theory. In this talk, I’ll discuss some progress on this question for algebraic vector bundles of rank 2 over smooth affine fourfolds. As a consequence, I will deduce some cohomological classification results (e.g., over the complex numbers, there are exactly 9 isomorphism classes of rank 2 vector bundles over the complement of a smooth degree 3 hypersurface in P^4). This is joint work with Thomas Brazelton and Tariq Syed.