Title: Adapted complex structures II
Speaker: László Lempert
Speaker Info: Purdue University
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.Date: Saturday, February 21, 2015
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.