Sabir Gusein-Zade (Moscow State University)
sabir@mccme.ru
The starting point of the subject was the observation that the Poincaré series of the filtration on the ring of germs of functions on an irreducible plane curve singularity defined by orders of functions on the curve coincides with the zeta-function of the monodromy transformation of the singularity. Attempts to obtain generalizations of this result led to the problem of computing the Poincaré series of multi-index filtrations. It turns out to be connected with integration with respect to Euler characteristic over the projectivization of the space of functions and in some cases can be reduced to integration (with respect to Euler characteristic) over a space of divisors.
Joint work with A. Campillo and F. Delgado (Valladolid, Spain).