New examples of Collapsed Ricciflat Spaces
New examples of Collapsed Ricciflat Spaces

Ruobing Zhang, Stony Brook University
Fine Hall 314
In this talk, we will focus on the construction of new examples of collapsed Ricciflat spaces. A special case is to construct a family of hyperkähler metrics on a K3 surface such that they are collapsing to a closed interval. Geometrically, the regular collapsing fibers in our example are 3DHeisenberg (nilpotent) manifolds with almost flat metrics, while the singular collapsing fibers are 3D smooth manifolds which are singular S^1fibrations over T^2. Compared with the known examples of codimension1 and codimension2 collapsing, we will see how such a collapsing phenomenon is related to a general regularity problem.