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Calabi-Yau Manifolds Seminar

Speaker: Tim Knyazhevskiy

Title: An Introduction to Planar and Elliptic Curves

Abstract:
We follow Professor Noriko Yui's notes on Elliptic Curves and Formal Groups. Starting with affine and projective spaces over a field $K$ we consider affine curves and their associated homogeneous forms. We observe some of their properties and define $K$-rational points over each and how counts of these points relate. Moving onto elliptic curves we define the Weierstrass equation and some invariants of an elliptic curve. Using the Weierstrass equation and its variations we then see some results on the classification of elliptic curves by its invariants as well as the automorphism group of an elliptic curve.