报告题目 (Title)：Bezout, Cayley-Bacharach, and associativity of the group action on an elliptic curve (Bezout定理、Cayley-Bacharach定理，以及椭圆曲线上群作用的结合律)

报告人 (Speaker)： Peter van der Kamp 教授（La Trobe University, Australia）

报告时间 (Time)：2024年09月25日(周三) 15:30-17:00

报告地点 (Place)：校本部GJ303

邀请人(Inviter)：张大军 教授

主办部门：理学院数学系

报告摘要：

I will state Bezout’s theorem, and will explain how to determine the multiplicity of a point in the intersection of two plane curves (a la Fulton). I will then provide a geometric proof of the Cayley-Bacharach theorem, which is (only) based on Bezout’s theorem, and linear algebra. Some consequences are Pappus’s theorem, Pascal’s theorem, and the associativity of the group action on an elliptic curve.