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CIMPA SUMMER SCHOOL 2007
Singularities, Scientific Program
Speaker / Conferencier: Jose Seade (Universidad Nacional Autónoma de Mexico, Cuernavaca)
Title / Titre du cours Topology of isolated singularities in analytic spaces.
1) The local conical structure. Motivation with the example of
homogeneous singularities, where the arguments are simple and
explicit. Cases of complex plane curves (and its relation with
knots) and surfaces.
2) Milnor's fibration theorem for complex singularities.
3) Generalization of Milnor's theorem to meromorphic maps. (where
there is presently interesting research going on)
Speaker / Conferencier: ElZein (Universite de Nantes, Nantes)
Title / Titre du cours From Local Systems to Constructible Sheaves.
1) Thom-Whitney stratifications.
2) Constructible sheaves.
Local systems appears in Differential Geometry in the study of the cohomology
groups of the fibers (or
level sets) of a submersion $f: X \to Y$ reflecting the locally constant
structure of the topology of the fibers (and even the differentiable structure)
(Ehreshman's theorem).
In algebraic geometry the cohomolgy of the fibers of $f: X \to Y$ has a
structure known as a constructible sheaf. For smooth complex varieties a smooth
morphism induces a submersion on the differentiable underlying structures,
hence the constructible sheaf reduces to a local system in this case. For a
general morphism, Thom - Whitney results show that the base can be stratified
such that the cohomology groups of the fibers are locally constant when
restricted to each open strata. The sheaves satisfying such property are called
constructible on the base. The course will introduce such sheaves and explain
their importance in the study of algebraic varieties.
Speaker / Conferencier: Mutsuo OKA (Tokyo University of Science, Tokyo)
Title / Titre du cours: Plane curves, local and global geometry
1) Local singularity of plane curves: Puiseux expansion, resolution of
singularities
, especially toric modifications for non-degenerate singularities, dual graphs
2) Global geometry: moduli of plane curves with fixed degree and fixed
configurations of singularities,
fundamental group of the complement, dual curves etc.
Speaker / Conferencier: D. Mond ( University of Warwick, Coventry)
Title / Titre du cours Introduction to Singularities of Mappings.
This is a basic course assuming limited knowledge of singularity theory. Its central theme is the link
between the deformation theory, for right-left equivalence, of singular germs of analytic maps, and the topology
and geometry of their stable perturbations. I will explain a number of techniques for calculating invariants of
both types,with considerable focus on low-dimensional examples.
Speaker / Conferencier: S. Altinok (Adnan Menderes University, Aydin)
Speaker / Conferencier: J. P. Brasselet (Luminy Institude of Mathematics, Marseille)
Speaker / Conferencier: L. D. Trang (The Abdus Salam International Centre for Theoretical Physics, Trieste)
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