Conférencier: Frédéric Rochon, UQAM

We will explain how to construct new examples of complete Calabi-Yau manifolds of maximal volume growth on certain smoothings of Cartesian products of Calabi-Yau cones.  A description of the geometry at infinity will be given in terms of a compactification by a manifold with corners obtained through a suitable sequence of blow-ups.  A key analytical step in the construction of these Calabi-Yau metrics is to derive good mapping properties of the Laplacian on some suitable weighted Hölder spaces.   Our methods also produce Calabi-Yau metrics with an isolated conical singularity modelled on a Calabi-Yau cone distinct from the tangent cone at infinity, in particular yielding a transition behavior between different Calabi-Yau cones as conjectured by Yang Li.  This is used to exhibit many examples where the tangent cone at infinity does not uniquely specify a Calabi-Yau metric with exact Kähler form. This is a joint work with Ronan Conlon.