Lorenzo Foscolo (University College London) will speak in the differential geometry seminar on 23 October. The talk will be at 2pm in the Salle des Profs (9th floor of building NO). Lorenzo’s title is “Yang-Mills instantons and codimension-1 collapse” and his abstract is below.
I will discuss joint work with Calum Ross in which we construct large families of Yang-Mills instantons, i.e. solutions of the anti-self-duality equations of 4-dimensional gauge theory, on gravitational instantons with ALF (asymptotically locally flat) asymptotics. The latter are certain complete non-compact hyperkähler 4-manifolds which are prototypical examples of codimension-1 collapsing behaviour of special holonomy Ricci-flat manifolds. Our construction describes the behaviour of Yang-Mills instantons on ALF spaces in the collapsed limit where these 4-dimensional geometries are close to a 3-dimensional collapsed limit space. In this limit, the instantons are well approximated by superpositions of simple localised building blocks constructed out of monopoles on R^3.