Campinas (visiting Edinburgh)

Instanton bundles were introduced by Atiyah, Drinfeld, Hitchin and Manin in the late 1970s as the holomorphic counterparts, via twistor
theory, to anti-self-dual connections (a.k.a. instantons) on the sphere S^4. We will revise some recent results regarding some of the basic
geometrical features of their moduli spaces, and on its possible degenerations. We will describe the singular loci of instanton sheaves,
and how these lead to new irreducible components of the moduli space of stable sheaves on the projective space.