# Seminar: Algebraic Numbers, Galois Theory and Applications

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## Generalities

Organizer: Valentina Di Proietto
Date: Mondays, 4-6pm, Place: SR210/A3, Arnimallee 3

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First meeting: Monday, April 13, 4pm, Room SR210, Arnimallee 3

Algebraic numbers are complex numbers which are zeroes of a polynomial with rational coefficients. For example $\sqrt{2}, 2^{1/3}$, $i$ or $e^{\frac{2\pi i}{n}}$. In this seminar we want to study algebraic numbers in the context of modern algebra. The notion of an algebraic extension of fields is central. Galois theory describes all (separable) algebraic extensions of a given field using the language of group theory. We will first discuss the Galois theory for finite algebraic extensions. It depends on the prior knowledge of the participants of the seminar how extensive this first stage will be. We will then study several applications and generalizations.