Abstract:  We address the homogenization of the two-dimensional Dirac operator with position dependent mass. The mass is piecewise constant and supported on small pairwise disjoint inclusions evenly distributed along a periodic square lattice. Under rather general assumptions on geometry of these inclusions we prove that the corresponding family of Dirac operators converges in the norm resolvent sense as the lattice period goes to zero to the Dirac operator with a constant effective mass provided the masses in the inclusions are adjusted to the scaling of the geometry. We also estimate the speed of this convergence in terms of the scaling rates. This is a joint work with V. Lotoreichik (Prague).