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Singularity Theory and Bifurcations

Objective

The aim of this project is a wide range of research in the Singularity Theory and in the Theory of Bifurcations. These fields are closely adjacent to a number of various problems of calculus, algebraic geometry, and 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 Theory of Bifurcations 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 two INTAS Projects: Investigations in singularity theory (94-4373, 1995-1997) and Topology and analysis of discriminant sets (96-0713, 1997-1999). Both INTAS Projects were coordinated by the coordinator of this Project Professor 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 200 papers were published or submitted for publication in framework of the INTAS Projects; some 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 European. 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 main directions of research in the framework of the Project are: "Study of global properties of spaces of generic geometric objects (knots, plane curves) and of invariants of these objects, study of problems of the complexity theory arising from the theory of discriminants", "Topological invariants of singular points of spaces and of maps, topology of polynomial maps and topology of moduli spaces and of bases of versal deformations", "Bifurcations in families of solutions of generalized Riemann-Hilbert Problems, signature techniques for computing topological invariants of semi-algebraic sets, topological study of functions with degenerate critical submanifolds", "Symplectic geometry methods in singularity theory", "Coverings of algebraic surfaces with A-D-E singularities and the generalized Chisini's Conjecture, deformations of non-complete intersection singularities and Gauss-Manin connections associated with them".

The Project brings together 5 research teams from the fSU:
Team 4:
Georgian Academy of Sciences, A.Razmadze Mathematical Institute (Georgia), 5 members, team leader G.N.Khimshiashvili; Team 5: Moscow State University (Russia), Faculty of Mechanics and Mathematics, 9 members, team leader S.M.Gusein-Zade;
Team 6: Moscow Aviation Institute (Russia), 7 members, team leader V.M.Zakalyukin;
Team 7: Steklov Mathematical Institute (Russia, Moscow), Department of Algebra, 4 members, team leader Vik.S.Kulikov;
Team 8: Independent University of Moscow, Mathematics Colledge (Russia, Moscow), 7 members, team leader V.A.Vassiliev;

- and 4 research teams from INTAS countries:
Team 1; The Netherlands, Universiteit Utrecht, Mathematisch Instituut, 8 members, team leader, the Coordinator of the Project D.Siersma;
Team 2: Germany, University of Hannover, Institute of Mathematics, 5 members, team leader W. Ebeling;
Team 3: France, CNRS, 6 members, team leader J.P. Brasselet;
Team 9: Great Britain, University of Liverpool, 6 members, team leader J.Bruce.

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Coordinator

Universiteit Utrecht

Address

Budapestlaan 6
3508 Ta Utrecht

Netherlands

Administrative Contact

Dirk SIERSMA (Professor)

Participants (8)

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Centre National de la Recherche Scientifique

France

Georgian Academy of Sciences

Georgia

Independent University of Moscow

Russia

M.V. Lomonosov Moscow State University

Russia

Moscow Aviation Institute

Russia

Russian Academy of Sciences

Russia

University of Liverpool

United Kingdom

Universität Hannover

Germany

Project information

Grant agreement ID: INTAS-2000-00259

  • Start date

    1 July 2001

  • End date

    30 June 2003

Funded under:

IC-INTAS

Coordinated by:

Universiteit Utrecht

Netherlands