KASS seminar

Abstract: In this talk, I will discuss perturbation problems for canonical metrics (such as Hermite-Einstein metrics on vector bundles or constant scalar curvature metrics on Kähler manifolds), where the goal is to produce new such metrics from old, in perturbed situations. I will focus on certain “semistable” cases, where one is infinitesimally close to being able to solve the original equation, but does not actually have a solution to begin with. This results in an obstructed perturbation problem - solutions do not always exist. I will try to highlight what the new challenges are in this situation and techniques to overcome them, in order to produce solutions to the perturbed equations assuming a necessary algebro-geometric criterion. This is based on joint works with Tipler, Dervan and McCarthy, and Ortu.