September 10, 2017
TITLE: Quotients and hypersurfaces of model metrics
ABSTRACT: I shall outline basic techniques in understanding induced structures on U(1)-quotients and hypersurfaces of metrics with holonomy or Spin(7), following separate joint work with V. Apostolov and D. Conti. I shall discuss some explicit examples that have also been developed by B. Acharya, R. Bryant, and U. Fowdar.
September 9, 2016
TITLE: Manifolds with holonomy Sp(n)Sp(1)
ABSTRACT: This holonomy group from Berger’s list characterizes the class of quaternion-Kähler (or “nearly hyperkähler”) manifolds of real dimension 4n. Each such manifold M carries a parallel 4-form, and is Einstein but is not in general Kähler. In the case of positive scalar curvature, the twistor space (a 2-sphere bundle over M) is Kähler, and it is an open question as to whether the only complete examples are homogeneous. This topic provides fascinating links between complex and Riemannian geometry that illustrate the power of spinor and twistor methods.