Complex Calabi-Yau Threefolds with Boundary

Explore complex Calabi-Yau threefolds with boundary in this 56-minute lecture by Simon Donaldson from Imperial College London, presented at the University of Miami. Delve into joint work with Fabian Lehmann, examining 3-dimensional complex manifolds with nowhere-vanishing holomorphic 3-forms. Learn about the extension of Hitchin's local Torelli Theorem to manifolds with boundary, focusing on the new data of closed 3-forms on 5-dimensional boundaries. Discover the application of sub-elliptic and Nash-Moser theory in proving results for pseudoconvex boundaries, with discussions on potential finite-dimensional obstruction spaces. Gain insights into related boundary value problems for G2 structures in seven dimensions and explore fascinating connections to classical affine differential geometry in real dimension three.

Simon Donaldson, Imperial College London: Complex Calabi-Yau threefolds with boundary