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The geometry of field extensions

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If you have a question about this talk, please contact Valentin Hübner.

There is a simple analogy between the algebraic theory of field extensions and the topological theory of covering spaces: this is particularly nice when we consider function fields over the complex numbers. In the first half of the talk I will try and exhibit this analogy with some examples that are easy to visualize; this should be accessible to most undergraduates and should show the motivation behind the study of Riemann Surfaces. In the second half, I will try to make this analogy more precise and talk about maps of Riemann surfaces; this will be more suitable for those who already have some basic knowledge of these ideas.

This talk is part of the The Archimedeans (CU Mathematical Society) series.

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