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Singularities in Geometry and Topology
IRMA Lectures in Mathematics and Theoretical Physics Vol. 20

Singularities in Geometry and Topology

Strasbourg 2009

Vincent Blanlœil (IRMA, Strasbourg, France)
Toru Ohmoto (Hokkaido University, Sapporo, Japan)

ISBN print 978-3-03719-118-7, ISBN online 978-3-03719-618-2
DOI 10.4171/118
December 2012, 370 pages, softcover, 17 x 24 cm.
48.00 Euro

This volume arises from 5th Franco-Japanese Symposium on Singularities, held in Strasbourg in August 2009. The conference brought together an international group of researchers working on singularities in algebraic geometry, analytic geometry and topology, mainly from France and Japan. Besides, it also organized a special session, JSPS Forum on Singularities and Applications, which was aimed to introduce some recent applications of singularity theory to physics and statistics.

This book comprises research papers and short lecture notes on advanced topics on singularities. Some surveys on applications that were presented in the Forum are also added. Topics covered include 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.

Keywords: singularity theory, singularities, characteristic classes, Milnor fiber, jet schemes, equisingularity, intersection homology, knot theory, Hodge theory, Fulton–MacPherson bivariant theory, mixed weighted homogeneous, nearby cycles, vanishing cycles