Eugene Gorsky
Semigroups, compactified Jacobians and q,t-Catalan numbers
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.