Galois groups and monodromy in algebraic geometry

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• Matteo Verni, Institut de Mathématiques de Jussieu - Paris Rive Gauche
• Friday 31 January 2025, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Adrian Dawid.

Many interesting counting problems (e.g. how many lines are on a smooth cubic surface in P^3?) come with the additional natural question of: which kind of symmetries do these finitely many solutions have? Since before the 20th century, geometers have been thinking about the “Galois group” of such problems. Indeed there are two natural ways to produce such symmetries: by Galois theory of fields, and by monodromy of finite topological coverings. In this talk we will see that, in those enumerative problems formulated via algebraic geometry, these two coincide, creating a fascinating link between general topology and pure algebra. We will discuss this in action, in a few concrete examples.

This talk is part of the Junior Geometry Seminar series.

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