Computational Singularity Theory

Singularity theory is a very active field of research at the intersection of topology, analysis, differential and algebraic geometry, in parts also interacting with theoretical physics and arithmetic geometry. Roughly speaking, it is concerned with the (mostly local) study of properties at points where smoothness fails. Over the last decades, many algorithms have been developed to facilitate these tasks.

In this mini-course, I shall give an introduction into the topic with emphasis on compuational and experimental methods.