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Calabi-Yau Manifolds Seminar

Speaker: Kamryn Spinelli (Â鶹¹ÙÍø's University)

Title: An Introduction to Planar and Elliptic Curves, part II

Abstract: In this talk we will continue following Professor Noriko Yui's notes on Elliptic Curves and Formal Groups. Beginning with an elliptic curve $E$  we describe a geometric interpretation for a group law for $E(K)$  the set of $K$-rational points on $E$. We follow this with an arithmetic approach to the group law, covering a newer (Sander Zweger, 2024) proof for associativity for when $char(K) \neq 2, 3$. We finish with a consideration of the Hessian of $\tilde{E}$  and flex points on $\tilde{E}$ the projective curve associated to $E$.