
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
Workshops
 Workshop on Topology of Real Algebraic Varieties
January 610, 1997
(Organizers: S. Akbulut, G. Mikhalkin, O. Viro)
 Subanalytic and Pfaffian Geometry  March 1114, 1997
(Organizers: E. Beirstone, P. Milman)
 Valuations  March 31April 4, 1997
(Organizer: M. Spivakovsky)
 Geometry and Complexity  May
511, 1997
(Organizers: A. Khovanskii, A. Nabutovsky)
 Symplectic Geometry  June 23  27,
1997
(Organizers: Y. Eliashberg, B. Khesin)
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 recursiontheoretic 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:
 Regular and irregular singular points of linear differential
equations. Classical Stokes phenomena.
 Nonlinear Stokes phenomena. EcalleVoronin moduli.
 PhragmenLindelof theorem for functional cochains. Galois groups
and Stokes operators.
 Complex saddlenodes: analysis and topology.
 Desingularization theorem for vector fields. Topological classifiacation
of germs of real planar vector fields.
 Order of topologically sufficient jet. Desingularization in
the families.
 Nonaccumulation theorem for hyperbolic polycycles.
 Nonaccumulation theorem for elementary polycycles: ingredients
of the proof.
 Classical RiemannHilbert problem. Negative solution by Bolibrukh.
 Nonlinear RiemannHilbert problem.
 HilbertArnold problem and smooth normal forms for local families.
Kotova zoo.
 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. GuseinZade,
V. Zakalyukin)
 MiniCourse on Topological and Algebraic Invariants of Singular
Varieties (S. Cappell)

