A comparison of the eigenvalues of the Dirac and Laplace operator on the   two-dimensional torus
  We compare the eigenvalues of the Dirac and Laplace operator on a two-dimensional torus with respect to the trivial spin structure. In particular, we compute their variation up to order 4 upon deformation of the flat metric, study the corresponding Hamiltonian and discuss several families of examples. 
Ilka Agricola, Bernd Ammann, Thomas Friedrich