Geometric Analysis Seminar
ALF spaces and collapsing Ricci-flat metrics on the K3 surface.
Location: Hill 705
Date & time: Tuesday, 18 October 2016 at 3:00PM - 3:11PM
Lorenzo Foscolo, Stony Brook: The Kummer construction of Kähler Ricci-flat metrics on the (smooth 4-manifold underlying a complex) K3 surface provides the prototypical example of the formation of orbifold singularities in non-collapsing sequences of Einstein 4-manifolds. Much less is known about the structure of the singularities forming along sequences of collapsing Einstein metrics. I will describe the construction of large families of Ricci-flat metrics on the K3 surface collapsing to the quotient of a flat 3-torus by an involution. The collapse occurs with bounded curvature away from finitely many points. The geometry around these points is modelled by ALF gravitational instantons (i.e. complete noncompact hyperkähler 4-manifolds with decaying curvature and cubic volume growth).