ИСТИНА

It was found that in a number of cases Poincaré series of (natural) multi-index filtrations on spaces of functions are related (sometimes coincide) with monodromy zeta functions (or with Alexander polynomials). Up to now these relations have no intrinsic explanations. They were obtained by direct computations of the both sides of relations in the same terms and comparison of the obtained expressions. One way to understand reasons for these relations is to generalize them to some adjacent situations, say, to equivariant ones. One diffculty on this way was connected with the lack of notions of Poincaré series of multi-index filtrations in equivariant settings. We discuss some possible definitions of this sort and some relations between equivariant Poincaré series and equivariant topology of plane curves. The talk is mostly based on joint works with A.Campillo and F.Delgado.