### Friendly presentation of Elliptic curves and Galois representations

Pure Mathematics Postgraduate Seminar

16th March 2018, 4:30 pm – 5:40 pm

Howard House, 4th Floor Seminar Room

The two protagonists of this talk are elliptic curves and Galois groups.

I will define elliptic curves and explain why they are an abelian group; in particular I will focus on points of finite order, known as torsion points. Then I will talk about Galois groups and describe the Galois action on torsion points.

I will give several examples to show this phenomenon in the simplest cases, and finally I will mention some possible generalizations.

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