Gleb Smirnov (Université de Genève) : Anti-self-dual blowups

Given a 4-manifold, one may ask to describe the set of negative (resp., positive) square cohomology classes realized by anti-self-dual (resp., self-dual) harmonic forms. The point is that, in principle, this set is a smooth invariant of a manifold. How to approach this question in full generality is a challenging problem. Still, we have a little progress in the following specific scenario: If our 4-manifold contains a sphere of self-intersection (-1), the cohomology class dual to that sphere is indeed represented by an anti-self-dual harmonic form (for suitable Riemannian metric). This is a joint work with Sewa Shevchishin.