Lattice-to-continuum approximations at interfaces

In this talk we will consider certain lattice sums which occur, for
instance, in the study of magnetic forces across interfaces. If the
lattice parameter tends
to zero, these lattice sums converge to surface integrals. I will present
the main ideas of the proof which uses so-called modified unit cells.
Moreover, I will show how this approximation result can be applied in the
context of magnetic forces.