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Amazon logo 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.

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

Supplementary Notes on Elliptic Operators.


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


There are four graded homework assignments.


There are no exams.

Topics Covered

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

  1. Complex variable theory on open subsets of Cn. Hartog, simply pseudoconvex domains, inhomogeneous C. R.
  2. Theory of complex manifolds, Kaehler manifolds.
  3. Basic theorems about elliptic operators, pseudo-differential operators.
  4. Hodge Theory on Kaehler manifolds.
  5. Geometry Invariant Theory.


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