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 Özlem Imamoglu, which will start at 2pm.

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

Abstract

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.

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