Eugene Gorsky<br>
Semigroups, compactified Jacobians and q,t-Catalan numbers<br>

A. Campillo, F. Delgado and S. Gusein-Zade showed that the
semigroup
of a plane curve singularity determines the Alexander
polynomial (and the topological type)
of its link. J. Piontkowski used this semigroup to describe
cell decompositions
of the compactified Jacobians for a certain class of
singularities. I will review these results
and relate the Piontkowki's cell decomposition to the
combinatorics of the q,t-Catalan numbers
introduced by A. Garsia, J. Haglund and M. Haiman. 
The talk is based on a joint work with M. Mazin.