October  4, 2023

Singularity Theory and Geometry

January to June 1997

In 1997 The Fields Institute will sponsor a program in Singularity Theory and Geometry. All activities will take place during the period January to June 1997 at The Fields Institute in Toronto. The program will include workshops and graduate courses and several lecture series and seminars. The participation of graduate students and postdoctoral fellows will be an integral part of the program's activities. (All activities of The Fields Institute are subject to availability of funds.)

Organizing Committee

Edward Bierstone (University of Toronto), Askold Khovanskii (University of Toronto), Pierre Milman (University of Toronto), Alex Nabutovsky (University of Toronto), Mark Spivakovsky (University of Toronto)

Program Topics of Concentration

  • Geometric and topological applications of singularity theory
  • Resolution of singularities and subanalytic geometry
  • Fewnomials and subanalytic sets
  • Geometry and complexity


Related Events

Fields Institute Distinguished Lecture Series

  • Mikhael Gromov, Institute des Hautes Études Sciences
  • Vladimir I. Arnol'd, Université de Paris - Dauphine, University of Moscow

Graduate Courses (January - April 1997)

  • Differential topology and geometry from a recursion-theoretic viewpoint (A. Nabutovsky)
  • Fewnomials (A. Khovanskii)
  • Resolution of singularities (E. Bierstone or P. Milman)
  • Normal Forms, Limit Cycles, Desingularization and Bifurcations (Prof. Y. Ilyasmenko from Moscow) Dates: January 20 - February 9, 1997
    Following is a description of the topics:
    1. Regular and irregular singular points of linear differential equations. Classical Stokes phenomena.
    2. Nonlinear Stokes phenomena. Ecalle-Voronin moduli.
    3. Phragmen-Lindelof theorem for functional cochains. Galois groups and Stokes operators.
    4. Complex saddlenodes: analysis and topology.
    5. Desingularization theorem for vector fields. Topological classifiacation of germs of real planar vector fields.
    6. Order of topologically sufficient jet. Desingularization in the families.
    7. Nonaccumulation theorem for hyperbolic polycycles.
    8. Nonaccumulation theorem for elementary polycycles: ingredients of the proof.
    9. Classical Riemann-Hilbert problem. Negative solution by Bolibrukh.
    10. Nonlinear Riemann-Hilbert problem.
    11. Hilbert-Arnold problem and smooth normal forms for local families. Kotova zoo.
    12. Finite cyclicity of generic elementary polycycles.
  • Singularities of Functions on the Circle & Characteristic Classes of S'-Bundles (M. Kazarian)
  • Introduction to Singularity Theory and its Applications (S. Gusein-Zade, V. Zakalyukin)
  • Mini-Course on Topological and Algebraic Invariants of Singular Varieties (S. Cappell)