讲座内容：

We consider systems from 2D conformal field theory, e.g. super Liouville equations, super sinh-Gordon equations, posed on a closed Riemann surface. Depending on the structure of the equations and the topology of the surfaces, we obtain various existence results via variational approach, most of which were the first nontrivial solution in the theory. This is a joint project with A. Jevnikar and A. Malchiodi.