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ALF gravitational instantons and collapsing Ricci-flat metrics on the K3 surface

Kähler Geometry, Einstein Metrics, and Generalizations March 21, 2016 - March 25, 2016

March 25, 2016 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Lorenzo Foscolo (University College London)
Location: MSRI: Simons Auditorium
  • algebraic geometry and GAGA

  • mathematical physics

  • complex differential geometry

  • Kahler metric

  • Ricci flatness

  • 4-manifolds

  • gravitational instantons

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



The Kummer construction of Kähler Ricci-flat metrics on the 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

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