Mean field equations, hyperelliptic curves, and modular forms (I)


Chin-Lung Wang

13:30:00 - 14:30:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

The aim of these two talks is to give an introduction to the study the geometry of flat tori, especially the Green function on it when the torus varies in the moduli. There are three major players in this study, one is the classical Lame equation and its associated hyperelliptic curves. The second one is the non-linear mean field equation with singular source which has been studied extensively during the last two decades. It turns out that there is a beautiful link between these two subjects via Green functions. The resulting object is a new kind of modular forms which we consider to be the third major player in this theory. This is a joint work with Chang-Shou Lin.

For material related to this talk, click here.