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This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz theorem, and Vanishing theorems. Some results and tools on deformation and uniformization of complex manifolds are also discussed.
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English
English [CC]
FREE
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Description
Course content
- Functions of one Complex Variable Unlimited
- Cauchy Integral Formula (cont.) Unlimited
- The Inhomogeneous Cauchy-Riemann Equation in Several Variables, Hartog’s Theorem Unlimited
- Applying Hartog’s Theorem, Unlimited
- The Holomorphic Version of the Poincare Lemma Unlimited
- The Inverse Function Theorem and the Implicit Function Theorem for Holomorphic Mappings Unlimited
- Complex Manifolds: Affine and Projective Varieties Unlimited
- Complex Manifolds: Affine and Projective Varieties (cont.) Unlimited
- Sheaf Theory and Sheaf Cohomology Unlimited
- The DeRham Theorem for Acyclic Covers Unlimited
- Identification of Cech Cohomology Groups with the Cohomology Groups of the Dolbeault Complex Unlimited
- Linear Aspects of Symplectic and Kaehler Geometry Unlimited
- The Local Geometry of Kaehler Manifolds, Strictly Pluri-subharmonic Functions and Pseudoconvexity Unlimited
- The Ricci Form and the Kaehler Einstein Equation Unlimited
- The Fubini Study Metric on CPn Unlimited
- Differential Operators on Rn and Manifolds Unlimited
- Smoothing Operators, Fourier Analysis on the n-torus Unlimited
- Pseudodifferential Operators on Tn and Open Subsets of Tn, Unlimited
- Systems of Elliptic Operators and Elliptic Operators on Vector Bundles Unlimited
- Elliptic Complexes and Examples Unlimited
- Hodge Theory, the *-operator Unlimited
- Computing the *-operator Unlimited
- The *-operator in Kaehler Geometry Unlimited
- The *-operator in Kaehler Geometry (cont.) Unlimited
- The Symplectic Version of the Hodge Theory Unlimited
- The Symplectic Version of the Hodge Theory (cont.) Unlimited
- The Brylinski Conjecture and the Hard Lefchetz Theorem, Unlimited
- Basic Facts About Representations of SL(2,R) Unlimited
- Hodge Theory on Kaehler Manifolds Unlimited
- Hodge Theory on Kaehler Manifolds (cont.) Unlimited
- Actions of Lie Groups on Manifolds, Unlimited
- Symplectic Reduction Unlimited
- Kaehler Reduction and GIT Theory Unlimited
- Toric Varieties Unlimited
- The Cohomology Groups of Toric Varieties Unlimited
- Stanley’s Proof of the McMullen Conjecture Unlimited
Instructor
Massachusetts Institute of Technology
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