2006 Madrid

2006 MADRID

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Scientific report

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CIMPA-UNESCO-SPAIN School

New trends in Singularity Theory

Objectives :
We intend to introduce the students to some important new developments in Singularity Theory and related areas in Algebraic Geometry, and to provide them with the tools necessary for conducting research in these areas.

This aim will be achieved in a series of mini-courses, each one starting with classical material and taking the audience to the current state of art in the subject. The 5th course is a hand-on activity designed to teach the students how to use the powerful computer algebra system SINGULAR.

A second main objective of this school is to facilitate the contacts of the students coming from the South with a large number of mathematicians. This is achieved by organizing this School in Madrid just before the opening of the ICM 2006.

Scientific advisory board:
A. Dimca (Nice, France) and I. Luengo (Madrid, Spain), A. Campillo (Valladolid, Spain), Pi. Cassou-Noguès (Bordeaux, France), A. Melle (Madrid, Spain)

Organizers:
J. Fernandez de Bobadilla, M. Gonzalez, I. Luengo (Madrid, Spain)

Working languages:
English

Date and location :
August 14-21, 2006, Madrid, Spain

Scientific programme: (abstracts, pdf)

We plan to have the following mini-courses.

1. Topology of polynomials and low dimensional

algebraic geometry, by E. Artal Bartolo (Universidad de Zaragoza, Spain).

2. Normal Surface Singularities, by A. Némethi (Rényi Institute, Budapest, Hungary).

3. An introduction to motivic integration and its

applications, by W. Veys (K.U. Leuven, Belgium).

4. Elementary aspects of perverse sheaves and

applications, by A. Dimca (Université de Nice, France).

5. How to use SINGULAR to study singularities, by G. Pfister (Kaiserslautern University, Germany).

Prerequisites :
The students are expected to be familiar with the basics of Algebraic Topology and Algebraic Geometry. Previous contacts with singularities, homological algebra or sheaves would be a plus, but are not essential.