The aim of the project is a wide range of research in the Singularity Theory, study of bifurcations and monodromy. These fields are closely adjacent to a number of various problems of calculus, algebraic geometry, topology, ... During last decades Singularity Theory benefited a lot from using methods of calculus, algebraic geometry, topology, and also influenced researches in these traditional fields of mathematics. Singularity Theory and its applications traditionally developed within two-way influence and cooperation between the West European and fSU groups of researches. In this an important role was played by the European Singularity Network (now terminated) and by three INTAS Projects: Investigations in singularity theory (94-4373, 1995-1997) and Topology and analysis of discriminant sets (96-0713, 1997-1999), Singularity Theory and Bifurcations (00-0259, 2001- 2003). All three INTAS Projects were coordinated by the coordinator of this Project Prof.Dr. D.Siersma. He also played an important role in the coordination of the European Singularity Network.
In frames of those Projects and of the Network there were elaborated a number of problems in Singularity Theory and in Bifurcation Theory, there were obtained a number of new results (more than 300 papers were published or accepted for publication in framework of the INTAS Projects; many of them are joint papers of fSU and Western participants, prepared in the framework of the Projects) and there was created a good scientific environment for further cooperation between West European and fSU groups of researchers. The groups involved in the Project include the majority of active researchers in the Singularity Theory from the fSU and from West and Central Europe.
The Project is supposed to considerably extend the knowledge in the area by further developing existing problems and by studying a number of new ones on the base of cooperation between the groups. The Project brings together 5 research teams from the fSU: Independent Univ. of Moscow, Mathematics Colledge (Russia, Moscow), 6 members, team leader V.A.Vassiliev; Moscow State Univ. (Russia), Faculty of Mechanics and Mathematics, 7 members, team leader S.M.Gusein-Zade; Moscow Aviation Inst. (Russia), 8 members, team leader V.M.Zakalyukin; Steklov Mathematical Inst. (Russia, Moscow), 5 members, team leader Vik.S.Kulikov; Georgian Academy of Sciences, A.Razmadze Mathematical Inst. (Georgia), 5 members, team leader G.N.Khimshiashvili; - and 6 research teams from INTAS countries: The Netherlands, Univ. Utrecht, Mathematisch Inst., 9 members, team leader, the Coordinator of the Project D.Siersma; Germany, Univ. of Hannover, 9 members, team leader W.Ebeling; France, Marseille-Nice-Strasbourg Univ., 9 members, team leader J.P. Brasselet; Great Britain, Univ. of Liverpool, 9 members, team leader V.Goryunov; Spain, Univ. of Valladolid, 12 members, team leader A.Campillo; Poland, Inst. of Mathematics, Warsaw, 8 members, team leader S.Janeczko.