## a $j$-invariant?

Who?
Emre Sertöz (HU Berlin)
When?
2013/01/18, 13:00
Before the BMS Friday Colloquium by Prof. Özlem Imamoglu
Where?
Urania Berlin, at the BMS Loft (3rd floor)
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.