Courses:

Topics in Several Complex Variables >> Content Detail



Syllabus



Syllabus

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Texts


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.



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.

  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.


Grading


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


 








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