One of the main objectives of the GDRI is to contribute to integration of young mathematician, at PhD or Post-Doc levels or young teachers in universities. That will be realized through conferences, courses and workshops.
Aim of the GDRI is to gather the research teams working in singularity theory of algebraic or analytic varieties and maps between these varieties. The project includes the algebraic, topological and geometric aspects as well as analytic viewpoint related to differential systems coming from geometric objects.
Singularity theory has a long history, starting in XIXth century. From years 1950, it is recognized as a branch of mathematics, following fundamental works of Zariski, Whitney and Thom, then Arnold, Hironaka, Milnor, Pham...
During the last 30 years, the Singularity Theory has been enriched with new and powerful technical tools like D-modules, intersection homology, Hodge theory and more recently motivic integration. France, Japan and Vietnam played an important role in the development.
Objective of the GDRI is to transmit to young mathematicians, from the three countries, the most important tools and a global view on the subject, by bi- or tri lateral workshops, schools and conferences and through animation of an international network. Hope is to develop the existing relationships at the international level.
The main research themes are the following: local resolution and uniformisation, valuation theory, real and complex singularities of spaces and of maps, stratifications, intersection homology, characteristic classes, local and global invariants of singular varieties, applications of D-modules and Hodge theory to singularities, b-functions and vanishing cycles, analytic arcs and motivic integration, toric varieties, arrangements...