Multi-index filtrations and Poincaré series of singularities.

During the last years the Poincaré series (PS) was developped as a new
invariant of the topological type of a complex singularity, mainly in
low dimensional contexts. In most cases the PS provides a bridge between
invariants of different nature (e.g. topological, combinatorial or
algebraic). For example, for plane curve singularities the PS could be
seen as the algebraic version of the Alexander polynomial of the link.
Along the talk I will give a general view on the construction and
meaning of the PS in a general context together with some recent results
on the subject.