  In this talk we discuss sector decomposition. This is a method to disentangle
overlapping singularities through a sequence of blow-ups. We report on an
open-source implementation of this algorithm to compute numerically the Laurent
expansion of divergent multi-loop integrals. We also show how this method can
be used to prove a theorem which relates the coefficients of the Laurent series
of dimensionally regulated multi-loop integrals to periods.
