Courses:

Topics in Several Complex Variables >> Content Detail



Lecture Notes



Lecture Notes

The lecture notes were prepared by Jonathan Campbell, a student in the class. They are available as a single file (PDF - 1.4 MB) or mapped to the lecture topics below. The notes for lectures 16, 17, and 18 are from the Supplementary Notes on Elliptic Operators.


Lec #Topics
Complex Variable Theory on Open Subsets of Cn
1Functions of one Complex Variable, Cauchy Integral Formula, Taylor Series, Analytic Continuation (PDF)
2Cauchy Integral Formula (cont.), Inhomogeneous C.R. Equation, Riemann Equation in One Variable, Functions of Several Complex Variables (PDF)
3The Inhomogeneous Cauchy-Riemann Equation in Several Variables, Hartog's Theorem (PDF)
4Applying Hartog's Theorem, The Dolbeault Complex, Exactness of the Dolbeault Complex on Polydisks (PDF)
5The Holomorphic Version of the Poincare Lemma (PDF)
6The Inverse Function Theorem and the Implicit Function Theorem for Holomorphic Mappings (PDF)
Theory of Complex Manifolds, Kaehler Manifolds
7Complex Manifolds: Affine and Projective Varieties (PDF)
8Complex Manifolds: Affine and Projective Varieties (cont.) (PDF)
9Sheaf Theory and Sheaf Cohomology (PDF)
10The DeRham Theorem for Acyclic Covers (PDF)
11Identification of Cech Cohomology Groups with the Cohomology Groups of the Dolbeault Complex (PDF)
12Linear Aspects of Symplectic and Kaehler Geometry (PDF)
13The Local Geometry of Kaehler Manifolds, Strictly Pluri-subharmonic Functions and Pseudoconvexity (PDF)
14The Ricci Form and the Kaehler Einstein Equation (PDF)
15The Fubini Study Metric on CPn (PDF)
Elliptic Operators and Pseudo-differential Operators
16Differential Operators on Rn and Manifolds (PDF)
17Smoothing Operators, Fourier Analysis on the n-torus (PDF)
18Pseudodifferential Operators on Tn and Open Subsets of Tn, Elliptic Operators on Compact Manifolds (PDF)
Hodge Theory on Kaehler Manifolds
19Systems of Elliptic Operators and Elliptic Operators on Vector Bundles (PDF)
20Elliptic Complexes and Examples (PDF)
21Hodge Theory, the *-operator (PDF)
22Computing the *-operator (PDF)
23The *-operator in Kaehler Geometry (PDF)
24The *-operator in Kaehler Geometry (cont.) (PDF)
25The Symplectic Version of the Hodge Theory (PDF)
26The Symplectic Version of the Hodge Theory (cont.) (PDF)
27The Brylinski Conjecture and the Hard Lefchetz Theorem, Hodge Theory on Riemannian Manifolds (PDF)
28Basic Facts About Representations of SL(2,R), SL(2,R) Modules of Finite H-type (PDF)
29Hodge Theory on Kaehler Manifolds (PDF)
30Hodge Theory on Kaehler Manifolds (cont.) (PDF)
Geometric Invariant Theory
31Actions of Lie Groups on Manifolds, Hamiltonian G Actions on Symplectic Manifolds (PDF)
32Symplectic Reduction (PDF)
33Kaehler Reduction and GIT Theory (PDF)
34Toric Varieties (PDF)
35The Cohomology Groups of Toric Varieties (PDF)
36Stanley's Proof of the McMullen Conjecture (PDF)

 








© 2010-2021 OpenCollege.com, All Rights Reserved.
Open College is a service mark of AmeriCareers LLC.