Abstract:

We will give an explicit construction of a solution to the mean field equation on hyperelliptic curves with respect to the canonical metric. In the first part of the talk, I will briefly review the notion of the canonical metric and motivate the problems we studied. In the second part of the talk, I will give an explicit solution of a solution to the MFE using an algebraic construction under certain algebraic conditions. In the end of the talk, I will present the future work in this direction.