Speaker: Nick Rekuski (Michigan State University)

Title: Wall-Crossing for Tilt Stability

Abstract: To study a vector bundle on an algebraic variety, we first decompose it into stable bundles---similar to the composition series of a group---then study the associated stable bundles. Recent developments have generalized the notion of a stable vector bundle to give a continuous family of stability conditions called the stability manifold. For surfaces, the structure of the stability manifold is well understood and can be used to give new results about vector bundles on surfaces. However, in higher dimensions, the stability manifold is not as well understood. In this talk, we give a structural result for the stability manifold in higher dimensions and then apply it to study vector bundles on projective space.