Singularities and Foliations. Geometry, Topology and Applications

1. Front Matter

   Pages i-xi

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2. Lecture Notes: Geometry, Topology, and Algebraic Aspects of Singularities

   1. Front Matter

      Pages 1-1

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   2. Combinatorial Models in the Topological Classification of Singularities of Mappings

      • J. J. Nuño-Ballesteros

      Pages 3-49

   3. Topology of Real Singularities

      • Nicolas Dutertre

      Pages 51-88

   4. Equisingularity and the Theory of Integral Closure

      • Terence Gaffney

      Pages 89-131

3. Surveys Papers on Advances in Foliations and Singularity Theory: Topology Geometry and Applications

   1. Front Matter

      Pages 133-133

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   2. A Brief Survey on Singularities of Geodesic Flows in Smooth Signature Changing Metrics on 2-Surfaces

      • N. G. Pavlova, A. O. Remizov

      Pages 135-155

   3. Orbital Formal Rigidity for Germs of Holomorphic and Real Analytic Vector Fields

      • Jessica Angélica Jaurez-Rosas

      Pages 157-180

   4. On Singular Holomorphic Foliations with Projective Transverse Structure

      • Bruno Scárdua

      Pages 181-228

   5. Disentanglements of Corank 2 Map-Germs: Two Examples

      • David Mond

      Pages 229-258

   6. Singular Fibers of Stable Maps of Manifold Pairs and Their Applications

      • Osamu Saeki, Takahiro Yamamoto

      Pages 259-294

   7. A Global View on Generic Geometry

      • María del Carmen Romero Fuster

      Pages 295-325

   8. Equisingularity

      • Lê Dũng Tráng

      Pages 327-345

   9. On the Factorization of the Polar of a Plane Branch

      • A. Hefez, M. E. Hernandes, M. F. H. Iglesias

      Pages 347-362

   10. Local Zeta Functions for Rational Functions and Newton Polyhedra

       • Miriam Bocardo–Gaspar, W. A. Zúñiga–Galindo

       Pages 363-385

   11. Symbolic Powers of Ideals

       • Hailong Dao, Alessandro De Stefani, Eloísa Grifo, Craig Huneke, Luis Núñez-Betancourt

       Pages 387-432

   12. Some Open Problems in Complex Singularities

       • José Seade

       Pages 433-456

4. Selected Papers in Foliations and Singularity Theory

   1. Front Matter

      Pages 457-457

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   2. A Comprehensive Approach to the Moduli Space of Quasi-homogeneous Singularities

      • Leonardo M. Câmara, Bruno Scárdua

      Pages 459-487

   3. On the Roots of an Extended Lens Equation and an Application

      • Mutsuo Oka

      Pages 489-511

This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

• Singularities
• Equisingularity
• Milnor Fibration
• Foliations
• Mappings
• Conference Proceedings
• Research
• 58K05
• 58K15
• 58K35
• 58K60
• 32S05
• 32S15
• 32S55
• 32S65

• ICMC, University of São Paulo, São Carlos, Brazil

  Raimundo Nonato Araújo dos Santos, Marcelo J. Saia

• Department of Mathematics, Federal University of Paraíba, João Pessoa, Brazil

  Aurélio Menegon Neto

• Mathematics Institute, University of Warwick, Coventry, United Kingdom

  David Mond

• Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, Cuernavaca, Mexico

  Jawad Snoussi

Raimundo Nonato Araújo dos Santos is an Associate Professor at the Institute of Mathematics and Computer Sciences of the University of São Paulo, Brazil. He holds a PhD in Mathematics (Singularity Theory) from the University of São Paulo (2002), with studies in Catastrophe Theory at the Northeastern University, in the USA. His research is on the fields of geometry and topology of real and complex singularities, real and complex Milnor fibrations, and topology of polynomial mappings at infinity.

Aurelio Menegon Neto is an Adjunct Professor at the Federal University of Paraíba, Brazil. He holds a PhD in Mathematics from the National Autonomous University of Mexico (UNAM) and did post-doc studies at the Institute of Mathematics and Computer Sciences of the University of São Paulo, Brazil, and UNAM, Mexico. His field of research is Singularity Theory, more specifically on the topology of real and complex manifolds and singularities in differential applications.

David Mond is a Full Professor at the Mathematics Institute of the University of Warwick, England. He did his PhD in Liverpool (1982), England, and has held several appointments in institutions such as University of Los Andes (Colombia), National University (Colombia), University of Seville (Spain) and Institut des Hautes Etudes Scientifiques (France). He is also co-editor of "Singularity Theory and its Applications", published with Springer, and has published over 40 papers and lecture notes on this field.

Marcelo J. Saia is a Full Professor at the Institute of Mathematics and Computer Sciences of the University of São Paulo, Brazil. He did his PhD at the University of São Paulo (1991), with studies at the University of Liverpool, England. His current research is focused on Singularity and Catastrophe Theory, more specifically on singularities of differential applications; singularities, dynamical systems and geometry; and topology of singular manifolds.

 Jawad Snoussi isa Full Researcher at the Institute of Mathematics of the National Autonomous University of Mexico (UNAM). He doctored in Mathematics at University of Provence (Aix-Marseille 1), France, in 1998, with studies at the Institute of Mathematics and Computer Sciences of the University of São Paulo, Brazil; at the Institute of Mathematics of the UNAM, Mexico; at the University of Lisbon, Portugal; and at the Internacional Center for Theoretical Physics, Italy. His research field is the local study of singularities of complex analytic spaces and real and complex analytic maps.

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