Woensdag 11 februari 2009
Spreker: 
Sabir GuseinZade (Moscow State University)

Titel: 
Poincare series of multiindex filtrations and their generalizations

Tijd: 
11:00  12:00

Plaats: 
HG00.062

Vanaf kwart voor 11 is er koffie en thee voor de zaal.
Abstract
For a multiindex filtration on a vector space (e.g. on the ring of germs
of functions on a variety) one can define a notion of the Poincare series,
generalizing the usual one for a oneindex filtration (the generating
series for the dimensions of the consecutive factors). (The definition is
not very straightforward.) The Poincare series can be written as a certain
integral with respect to the Euler characteristic. It appears that the
Poincare series of a natural filtration associated to a plane curve
singularity coincides with the classical monodromy zetafunction of the
corresponding equation. There is a generalizations of this notion for an
equivariant situation. Another generalization is obtained by substituting
the usual Euler characteristic by a generalized one. This leads to the
Poincare series depending on an additional variable. E.Gorsky has found
that, for irreducible plane curve singularities, the generalized Poincare
series is strongly connected with the generating series of the
HeegaardFloer homologies of the corresponding algebraic knot (defined by
P.Ozsvath and Z.Szabo).