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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
11
votes
Ways to prove the fundamental theorem of algebra
I'm partial to Milnor's proof in Topology from the Differentiable Viewpoint, a slightly simpler variant of the "every complex non-constant polynomial $p$ is surjective" proof given above, published so …