|Location:||MSRI: Simons Auditorium|
Compact 6-dimensional nearly Kähler manifolds are the cross-sections of Riemannian cones with G2 holonomy. In particular they are Einstein manifolds with positive scalar curvature and admit real Killing spinors. Viewing Euclidean 7-space as the cone over the round 6-sphere endows the 6-sphere with a nearly Kähler structure which coincides with the standard G2-invariant almost complex structure induced by octonionic multiplication. A long-standing problem has been the question of existence of complete nearly Kähler 6-manifolds besides the four known homogeneous ones. We resolve this problem by proving the existence of an exotic (inhomogeneous) nearly Kähler structure on the 6-sphere and on the product of two 3-spheres. This is joint work with Mark Haskins, Imperial College London.