Complex manifold

Related lectures (30)

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Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Explores necessary and sufficient optimality conditions for local minima on manifolds, focusing on second-order critical points.

Covers conformal blocks and their significance in complex structures and moduli spaces.

Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores geodesics in the Wasserstein space, emphasizing constant speed geodesics and their properties.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.