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.)
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
- Workshop on Topology of Real Algebraic Varieties--
January 6-10, 1997
(Organizers: S. Akbulut, G. Mikhalkin, O. Viro)
- Subanalytic and Pfaffian Geometry -- March 11-14, 1997
(Organizers: E. Beirstone, P. Milman)
- Valuations -- March 31-April 4, 1997
(Organizer: M. Spivakovsky)
- Geometry and Complexity -- May
(Organizers: A. Khovanskii, A. Nabutovsky)
- Symplectic Geometry -- June 23 - 27,
(Organizers: Y. Eliashberg, B. Khesin)
Fields Institute Distinguished Lecture Series
- Mikhael Gromov, Institute des Hautes Études Sciences
- Vladimir I. Arnol'd, Université de Paris - Dauphine, University
Graduate Courses (January - April 1997)
- Differential topology and geometry from a recursion-theoretic viewpoint
- 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. Ecalle-Voronin moduli.
- Phragmen-Lindelof 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
- Nonaccumulation theorem for hyperbolic polycycles.
- Nonaccumulation theorem for elementary polycycles: ingredients
of the proof.
- Classical Riemann-Hilbert problem. Negative solution by Bolibrukh.
- Nonlinear Riemann-Hilbert problem.
- Hilbert-Arnold problem and smooth normal forms for local families.
- 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,
- Mini-Course on Topological and Algebraic Invariants of Singular
Varieties (S. Cappell)