title: Singularities -- How to find them and how to get rid of them!
Abstract:
Singular points of algebraic varieties and complex spaces are often perceived as an obstacle to applying standard methods. But they are
beautiful and interesting objects in their own right and come with rich structure. They certainly merit a deeper study, which historically had a focus on hypersurfaces and complete intersections. In this talk, we will first discuss an algorithmic approach for parallel singularity detection and then we go on to methods for relating suitable smooth objects to a given singularity -- namely smoothings and desingularization. Along the way, we will encounter also new results on non-isolated singularities, which are simple in the sense of Arnold -- something that cannot occur for hypersurfaces and complete intersections.