Sondertermin: New invariants of plane curve singularities

Abstract: We describe certain invariants constructed from Euler numbers of Hilbert schemes of points on curves, first introduced by Pandharipande and Thomas. We show that these invariants describe the multiplicities of certain geometric strata in the versal deformation of the singularity, and explain how they may be used to prove a conjecture of Göttsche on counting curves on surfaces. We conjecture a relation between these invariants and the Khovarov-Rozansky homology of the link of the singularity.