Emre Sertöz (HU Berlin)

2013/01/18, 13:00

Before the BMS Friday Colloquium by Prof. Özlem Imamoglu

Before the BMS Friday Colloquium by Prof. Özlem Imamoglu

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.