### Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

### Texts

Hormander, L. *An Introduction to Complex Analysis in Several Variables*. 2nd revised ed. Vol. 7, *North-Holland Mathematical Library*. Amsterdam-London: North-Holland Publishing Co. ; New York, NY: American Elsevier Publishing Co., Inc., 1973. ISBN: 0444105239.

Griffiths, P., and J. Harris. *Principles of Algebraic Geometry*. New York, NY: John Wiley and Sons, 1978. ISBN: 0471327921.

Supplementary Notes on Elliptic Operators.

### Prerequisites

The prerequisites for this class are Functions of a Complex Variable (18.112) and Geometry of Manifolds (18.965).

### Homework

There are four graded homework assignments.

### Exams

There are no exams.

### Topics Covered

There are five segments in this course, each involving about 6 to 8 lectures.

- Complex variable theory on open subsets of C
^{n}. Hartog, simply pseudoconvex domains, inhomogeneous C. R. - Theory of complex manifolds, Kaehler manifolds.
- Basic theorems about elliptic operators, pseudo-differential operators.
- Hodge Theory on Kaehler manifolds.
- Geometry Invariant Theory.

### Grading

The grade for this class is based on the four homework assignments.