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 IRMA Lectures in Mathematics and Theoretical Physics 2012; 370 pp; softcover Volume: 20 ISBN-10: 3-03719-118-X ISBN-13: 978-3-03719-118-7 List Price: US$62 Member Price: US$49.60 Order Code: EMSILMTP/20 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. A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in various approaches to singularities. Table of Contents A. Joets -- Optical caustics and their modelling as singularities (JSPS Forum) H. A. Hamm -- On local equisingularity S. Ishii, A. Sannai, and K.-i. Watanabe -- Jet schemes of homogeneous hypersurfaces T. Koike -- Singularities in relativity (JSPS Forum) Y. Matsumoto -- On the universal degenerating family of Riemann surfaces Y. Nakamura and S. Tajima -- Algebraic local cohomologies and local $$b$$-functions attached to semiquasihomogeneous singularities with $$L(f)=2$$ T. Ohmoto -- A note on the Chern-Schwartz-MacPherson class M. Oka -- On mixed projective curves T. Okuma -- Invariants of splice quotient singularities O. Riemenschneider -- A note on the toric duality between $$A_{n,q}$$ and $$A_{n,n-q}$$ J. Schürmann -- Nearby cycles and characteristic classes of singular spaces T. Suwa -- Residues of singular holomorphic distributions (lecture) S. Watanabe -- Two birational invariants in statistical learning theory (JSPS Forum) T. Yasuda -- Frobenius morphisms of noncommutative blowups S. Yokura -- Bivariant motivic Hirzebruch class and a zeta function of motivic Hirzebruch class (lecture) M. Yoshinaga -- Minimality of hyperplane arrangements and basis of local system cohomology