A Floer Homology for the Dirac-Geodesic Problem.

In this talk we will discuss the problem of existence of non-trivial Dirac-Geodesics. This problem comes from the super-symmetric non-linear Sigma model in physics. The problem is firstly stated for the case of surfaces then we reformulate it for loops. We sketch the basic idea of constructing the homology and its computation and how it can be used to prove existence of non-trivial Dirac-Geodesics.