I'm considering applying to a master's program based on complex analysis, but I understand that there are probably no, or very few, graduate programs centered on pure [multivariable] complex analysis. So I would like to see what interesting fields of mathematics I might choose to specialize in, which fairly heavily depend on this field of mathematics, even if it's applied mathematics (dynamical systems could probably be one example, and from pure math fractal geometry appears to be a good example). Would appreciate your input.
Which fields of mathematics heavily depend on complex anaysis?
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complex-analysis
soft-question
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1At least single variable complex analysis is important for modern number theory. – 2017-01-22
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1Among possibly surprising connections, complex variables is important in investigating circle packings, a very discrete sort of problem. Here is [a review by Philip Bowers](http://www.math.fsu.edu/~aluffi/archive/paper356.pdf) of a book length introduction to the subject by Ken Stephenson. By the time you run the gauntlet of first- and second-year graduate classes, you will have a better grasp of the kinds of problems that interest you sufficiently. – 2017-01-22