Speaker: Ziming Shi, University of California – Irvine

Title: Deformation theory of complex structures on manifolds with boundary

Abstract: In the late 1970s, R. Hamilton initiated a program to extend the Kodaira-Spencer's elliptic deformation theory of complex structures to manifolds with boundary. The stable case can be stated as follows. Let D be a relatively compact domain in a complex manifold M with certain complex analytic geometry. Assume H1(D,T) = 0, where T is the holomorphic tangent bundle of M. Given a formally integrable almost complex structure X defined on the closure D, and provided that X is sufficiently close to the standard complex structure on M, does there exist a complex/holomorphic coordinate that is compatible with X? In other words, does there exist a diffeomorphism from D into M tha...