This volume is the proceedings of the 12th International Research Institute of the Mathematical Society of Japan, held during 2003. The papers cover several important topics in singularity theory, including survey on motivic integrations, Thom polynomials, complex analytic singularity theory, generic differential geometry, etc.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.

Readership

Graduate students and research mathematicians interested in theory of singularities and catastrophe theory.

Table of Contents

• E. A. Bartolo, J. C. Ruber, J. I. Cogolludo-Agustĭn, and M. A. Marco-Buzunăriz -- Invariants of combinatorial line arrangements and Rybnikov's example
• A. Davydov -- On time averaged optimization of dynamic inequalities on a circle
• L. M. Féher and R. Rimányi -- Thom polynomial computing strategies. A survey
• V. Goryunov and S. H. Man -- The complex crystallographic groups and symmetries of \(J_{10}\)
• C. Hertling -- \(tt^*\) geometry and mixed Hodge structures
• M. Kazarian -- Thom polynomials
• K. Kurdyka and A. Parusiński -- Quasi-convex decomposition in o-minimal structures. Application to the gradient conjecture
• A. Libgober -- Homotopy groups of complements to ample divisors
• D. Matei -- Massey products of complex hypersurface complements
• V. S. Matveev -- On degree of mobility for complete metrics
• P. Mormul -- Valuations and moduli of Goursat distributions
• C. Murolo and D. Trotman -- Semidifférentiabilité et version lisse de la conjecture de fibration de Whitney
• J. J. Nuño-Ballesteros -- Submanifolds with a nondegenerate parallel normal vector field in euclidean spaces
• O. M. Abderrahmane -- Weighted homogeneous polynomials and blow-analytic equivalence
• A. Parusiński -- Characteristic classes of singular varieties
• G. M. Polotovskiy -- On the classification of 7th degree real decomposable curves
• M. J. Saia and L. M. Soares -- \(\mathcal A\)-topological triviality of map germs and Newton filtrations
• V. D. Sedyh -- On the topology of symmetry sets of smooth submanifolds in \(\mathbb{R}^k\)
• M. A. S. Ruas and J. N. Tomazella -- An infinitesimal criterion for topological triviality of families of sections of analytic varieties
• J. Sotomayor and R. Garcia -- Lines of principal curvature near singular end points of surfaces in \(\mathbb{R}^3\)
• D. Trotman and L. Wilson -- \(r\) does not imply \(n\) or \((npf)\) for definable sets in non polynomially bounded o-minimal structures
• M. Vaquié -- Valuations and local uniformization
• W. Veys -- Arc spaces, motivic integration and stringy invariants
• Y. Yamada -- Finite Dehn surgery along A'Campo's divide knots