This volume arises from the Fifth Franco-Japanese Symposium on Singularities, held in Strasbourg in August 2009. The conference brought together an international group of researchers, mainly from France and Japan, working on singularities in algebraic geometry, analytic geometry and topology. The conference also featured the JSPS Forum on Singularities and Applications, which aimed to introduce some recent applications of singularity theory to physics and statistics.

This book contains research papers and short lecture notes on advanced topics on singularities. Some surveys on applications that were presented at the JSPS Forum are also included. Among the topics covered are splice surface singularities, \(b\)-functions, equisingularity, degenerating families of Riemann surfaces, hyperplane arrangements, mixed singularities, jet schemes, noncommutative blow-ups, characteristic classes of singular spaces, and applications to geometric optics, cosmology, and learning theory.

Graduate students who wish to learn about various approaches to singularities, as well as experts in the field and researchers in other areas of mathematics and science, will find the contributions to this volume a rich source for further study and research.