Surfaces singularities – SUSI

The main objective of our project is to unify three important but presently diverging domains of research in singularity theory : deformation theory, metric theory and arc space theory. In the last years, these three domains developed separately and mostly in complex dimension two, affording us a consequent basis of analysis in this dimension. For this reason, we will concentrate on the case of complex surface singularities, in which all the members of our team are experienced researchers, but with complementary skills, going from the geometric and topological to the algebraic or algorithmic ones. Another objective of our project is to prove important results or existing conjectures using the relations discovered between the three domains. Therefore, our ambition is to contribute to the creation of strong ties between these domains of singularity theory in complex dimension two and to solve several conjectures.