### Friendly presentation of Elliptic curves and Galois representations

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.

*Organiser*: Quantum Information Theory Group

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*Organisers*: Ben Barrett, Radhika Gupta, Alex Malcolm, Leonid Monin

*Organisers*: Kevin Grace, David Ellis, Brendan Murphy

*Organisers*: Thomas Jordan, Rhiannon Dougall, Demi Allen

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*Organisers*: Tyler Helmuth, Ofer Busani

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