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This book contains a collection of papers covering recent progress in a number of areas of singularity theory. Topics include blow analyticity, recent progress in the research on equivalence relations of maps and functions, sufficiency of jets, and the transversality theorem. . Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood. Singularity theory may unify these studies and a survey based on this viewpoint is presented in which a new notion of weak solution is introduced. There are also reports on the recent progress in Zariski's conjecture on multiplicities of hypersurfaces, transcendency of analytic sets and on the topology of weighted homogeneous polynomials. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory.
This volume presents the proceedings of a meeting held in Sapporo (Japan) at Hokkaido University on singularities and arrangements of hyperplanes. Participants from the international community presented their research on singularities of curves, characteristic classes of singular varieties, $D$-modules, motives, resolution of singularities, Milnor fibration, Enriques diagrams, Hilbert schemes, and log-canonical singularities.
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The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
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Lists for 19 include the Mathematical Association of America, and 1955- also the Society for Industrial and Applied Mathematics.
Lists for 19 include the Mathematical Association of America, and 1955- also the Society for Industrial and Applied Mathematics.