Volker Branding (Universität Wien)
We will discuss the functional of the supersymmetric nonlinear sigma model as a geometric variational problem. Its critical points couple the harmonic map equation to spinor fields, these became known as Dirac-harmonic maps and variants thereof in the mathematics literature. We will give an overview of the current known results on the geometric and analytic properties of the critical points. Finally, we will address the question how to derive existence results for the latter.