# Calendar

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