Office: 4-112 Mathematics Building
Dept. Phone: (631)-632-8290
Time and place: Tu-Th 11:30-12:50 4-130 Math Tower
We will use the text `Harmonic Measure' by by John Garnett and Don Marshall, , published by Cambridge University Press.
This is a second course in one complex variable. We start with the hyperbolic metric on the disk, the Dirichlet problem on general planar domains and extremal length. We then will discuss the boundary behavior of conformal maps and connections to other topics such as quasiconformal maps, probability theory and fractal geometry. By skipping some sections and just summarizing others, I hope to reach the presentation of Makarov's theorems on the dimension of harmonic measure on simply connected plane domains.
Here is a tentative lecture schedule . It is likely that we will deviate from this as the semester progresses.
There will be problem sets, a midterm and a final.
Although it is not required, you may wish to consider writing up your solution in TeX, since eventually you will probably use this to write your thesis and papers. Here are a sample LaTex file and what the resulting output looks like . You can use the first file as a template to create your own TeX files. Numerous guides exist online that give the basic rules and commands.
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Link to history of mathematics