Victoria Gu
Abstract:
An elliptic curve over a field k is a smooth projective curve of genus 1 with a distinguished point O. With Riemann-Roch theorem and assuming that char(K) $\neq$ 2,3 , every elliptic curve can be represented by $y^2 = x^3 + Ax + B,$ for $A , B \in k$. In this talk, we give an overview of the uniformisation theorem, which states that any elliptic curve defined over $\mathbb{C}$ is isomorphic to $\mathbb{C}/L$ for some lattice $L$. We start by looking at maps that carry $\mathbb{C}/L$ to $E(\mathbb{C})$ isomorphically. Then we look at two proofs of the inversion problem. The first proof uses the fact that j-invariant classifies elliptic curves over C up to isomorphism. The second proof is more concrete and is achieved via construction of a Riemann surface.
Pure Maths Seminar
UNSW Sydney
Wed, 05/08/2020 - 12:00pm
Zoom link: https://unsw.zoom.us/j/92916731416