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Galois Groups and Fundamental Groups

There are many formal analogies between the classical Galois theory of fields and the theory of covering spaces in algebraic topology. In this seminar we will see that, in certain situations over the complex numbers, this intuition can be turned into a theorem, using Riemann surfaces as a bridge between the two worlds. As an application of this theory, we will compute the absolute Galois group of the complex function field C(t). We will roughly follow the first three chapters of Szamuely's book "Galois Groups and Fundamental Groups" . No previous knowledge of covering spaces or Riemann surfaces will be required, as we will introduce these notions during the seminar. If you are already familiar with these, it will still be interesting for you to see how these notions interact from a Galois-theoretic viewpoint.

We will have an organizatorial meeting on February 10. The zoom link is here.

A detailed seminar program can be found here .

Distribution of the Talks:

The seminar will take place on Monday from 16.15 to 17.45. The zoom link for the meetings is here.