Periodic homogenization of non-local elliptic and parabolic operators of convolution type

The talk will be focused on homogenization problems for convolution type operators in periodic media. We will consider a family of operators obtained by the diffusive scaling of a given convolution type operator. It will be shown that for operators whose kernel has a finite second moment and satisfies uniform ellipticity conditions, the corresponding family admits homogenization and that the limit operator is a second order elliptic differential operator with constant coefficients.