What is ... a j-invariant?

This page hosts information on Emre Sertoz's talk "What is ... a j-invariant?" at the "What is ...?" seminar. The talk will take place on Friday, January 25, 1:15pm at the BMS Loft at Urania. This talk will help you better understand the talk by ÷zlem Imamoglu, which will start at 2pm.

We will not be ordering pizza this week because of the Kovalevskaya lunch.


The elliptic curves (or complex tori) can be parametrized in 2 different ways. The first method parametrizes lattices in the complex plane in a rather obvious way. The second parametrization gives to each elliptic curve a more geometric value in the sense that this value corresponds more closely to how the curve is embedded in the plane. Then there is a function mapping the first parametrization to the other. This function is called the j-invariant and it is a modular form of weight zero, where number theory comes to join geometry and algebra. We will discuss briefly what modular forms are and what a fundamental domain is--all the absolute basics you need to know.



Topic revision: r1 - 22 Jan 2013, MimiTsuruga
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