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The biennial meetings at São Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The tenth meeting, celebrating the 60th birthdays of Terence Gaffney and Maria Aparecida Soares Ruas, was a special occasion attracting the best known names in the area. This volume contains contributions by the attendees, including three articles written or co-authored by Gaffney himself, and survey articles on the existence of Milnor fibrations, global classifications and graphs, pairs of foliations on surfaces, and Gaffney's work on equisingularity.

Singularities (Mathematics)

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Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.

Singularities (Mathematics)

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Singularity theory is a broad subject with vague boundaries. It draws on many other areas of mathematics, and in turn has contributed to many areas both within and outside mathematics, in particular differential and algebraic geometry, knot theory, differential equations, bifurcation theory, Hamiltonian mechanics, optics, robotics and computer vision. This volume consists of two dozen articles from some of the best known figures in singularity theory, and it presents an up-to-date survey of research in this area.

Singularities (Mathematics) --- Congresses. --- Singularities (Mathematics) - Congresses.

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This 1998 book is both an introduction to, and a survey of, some topics of singularity theory; in particular the studying of singularities by means of differential forms. Here some ideas and notions that arose in global algebraic geometry, namely mixed Hodge structures and the theory of period maps, are developed in the local situation to study the case of isolated singularities of holomorphic functions. The author introduces the Gauss-Manin connection on the vanishing cohomology of a singularity, that is on the cohomology fibration associated to the Milnor fibration, and draws on the work of Brieskorn and Steenbrink to calculate this connection, and the limit mixed Hodge structure. This will be an excellent resource for all researchers whose interests lie in singularity theory, and algebraic or differential geometry.

Hodge theory. --- Singularities (Mathematics)

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Singularities (Mathematics) --- Geometry, Algebraic --- Singularitats (Matemàtica)