EVENT DETAILS AND ABSTRACT

Title: Adapted complex structures II
Speaker: László Lempert
Speaker Info: Purdue University
Brief Description:
Special Note:
Abstract:

Adapted complex structures, also known as Grauert tubes, first arose in the early 1990s in connection with the homogeneous complex Monge-Ampère equation, as complex structures on the tangent or cotangent bundle of a Riemannian manifold M (or on certain subsets of these bundles). They also arise in Lie theory, geometric quantization and in the study of semiclassical pseudodifferential operators.

Adapted complex structures can be viewed as complex structures on the phase space of M that are compatible with the natural symmetries of phase space, and this is the approach I will take in my lectures. I will discuss various definitions of these structures and their fundamental properties, such as existence, uniqueness, regularity; also the connection with the Monge-Ampère equation and with curvature estimates for the metric of M.