EVENT DETAILS AND ABSTRACT

Title: The geometry of noncompact Calabi-Yau manifolds
Speaker: Hans-Joachim Hein
Speaker Info: University of Nantes
Brief Description:
Special Note:
Abstract:

A Calabi-Yau manifold is a complex Kahler manifold with vanishing first Chern class. This seemingly innocent topological condition has many remarkable consequences. Of particular interest is Yau's 1978 landmark theorem showing that such manifolds, if compact, admit Ricci-flat Kahler metrics - a feat of nonlinear analysis, and one of very few general sources of solutions to the Einstein equations in Riemannian geometry. A longstanding question in the field asks for extensions of Yau's theorem to noncompact settings and particularly for the possible asymptotics of noncompact Ricci-flat manifolds at infinity or at a singularity. I will survey recent progress on this question, mainly based on the point of view that a detailed understanding of the Riemannian geometry of the problem is key to proving useful estimates.