Math 80380 (Topics in Complex Analysis)

The Complex Monge-Ampere Operator

Jeffrey Diller (click for contact info)
Time and place: MWF, 10:40-11:30 in 131 DeBartolo.

Abstract:  The real and imaginary parts of a holomorphic function of one complex variable are harmonic.   So begins a beautiful relationship between classical complex function theory and the (linear) Laplace equation in the plane.  In several complex variables, however, the Laplace operator and its associated potential theory are not so relevant.  Instead, one is led to consider the complex Monge-Ampere operator.  This course aims to tell the much more recent story of this non-linear operator and its applications to complex analysis and geometry. 

Text: I'm putting the books Pluripotential Theory by Klimek and The Complex Monge-Ampere Operator and Pluripotential Theory by Kolodziej on reserve in the math library.  The former is more elementary but also a little dated by now.  Mostly, however, I'll be following freely available notes and articles which I'll link to below.  In particular, for the first half of the semester, I'll lean particularly heavily on some course notes by Blocki.  And now I find I've been typing up some notes of my own, partly to clean up issues from lecture and partly just to make myself happy.  These aren't comprehensive, but they do include some extra detail and different presentation of many basic points.
Topics covered (the plan):
Possible other topics:
Now here's what actually happened:
If only I'd had more time, I would've
As it is, that's all folks.  Thanks for your attention.