INTAS Project  Call 2005

Singularities, Bifurcations and Monodromy

Start date             : Oct 1,  2006
Duration              : 24 months

Coordinator: Prof. dr. Dirk Siersma

Participants: (Main nodes and local coordinators)
The Netherlands, University Utrecht (Dirk Siersma)
Germany, Hannover University  (Wolfgang Ebeling)
France, CNRS (J.P. Brasselet)
Spain,  Universidad de Valadolid (A. Campilo)
United Kingdom, University of Liverpool (V. Goryunov)
Poland, Academy of Science (S. Janeczko)
Russia. Moscow, Steklov Institute (Vic. Kulikov)
Russia, MoscowAviation Institute (V. Zakalyukin)
Russia, Moscow State University (S. Gusein-Zade)
Russia, Moscow, Indepent University (V. Vassiliev)
Georgia, A.Ramadze Mathematical Institute (G. Khimshiashvili)

Research Programme  Singularities, Bifurcations and Monodromy:

The aim of the project is a wide range of research in the Singularity Theory, study of bifurcations and monodromy. The programme of the Project includes the following tasks and subtasks: see more in Research details:

Finite order invariants of maps of one-dimensional manifolds.

Subtasks: Finite order invariants of knots determined by graph invariants. Detecting link orientation by finite type invariants. Periodic and double periodic knots and links. Combinatorial formulas for invariants and cohomology of generic submanifolds.

Singularities and integrable systems.

Subtasks: Noncommutative Frobenius manifolds. Hurwitz spaces and integrable systems.

Topological and analytical invariants of singular spaces and maps.

Subtasks: Poincare series, monodromy and integration of motivic type. Indices of 1-forms and characteristic classes of singular varieties. Structures on Riemann surfaces. Applications of higher Bruhat orders and multiplicative intersection theory.

Global invariants of singularities.

Subtasks: Calculation of Thom polynomials. Global Legendre topology. Coexistence of real singularities.

Singularities of caustics and wave fronts related to geometric and applied problems.

Subtasks: Applications of wave fronts and caustics. Singularities of wave transition. Singularities in optimization.

Deformation problems in real algebraic geometry.

Subtasks: "Dif=Def" problem in real algebraic geometry. Real braid monodromy factorisations. Equisingular deformation of a complex singularity to real one.

Singularities of pairs on algebraic threefolds.

Subtasks: Compactifications of del Pezzo fibrations of small degrees. Dual complex associated to a resolution of singularities.

Logarithmic connections and multidimensional Picard-Fuchs systems.

Subtasks: Logarithmic connection and uniformization equations for $A_k$-singularities. LC for special type of divisors and multi-dimensional Picard-Fuchs systems of differential equations

Topological invariants of real algebraic maps and varieties.

Subtasks: Algebraic formulae for topological invariants of real varieties. Topology of real nonisolated singularities.


    May 31-June 2, 2007 : Geometry Days (Jozef Steenbrink 60 year); Nijmegen, The Netherlands

    June 4,5, 2007 : Singularity Days, ; Nijmegen, The Netherlands

    May 31-June 2, 2007 : Algebraic geometry and Computer Algebra (Gerhard Pfister 60year ) Kaiserslautern, Germany

    June 25-29, 2007 : Zeta Functions in Algebra and geometry ; Segovia, Spain

    July 4-6, 2007 : Singularity Conference (Terry Wall 70 year), Liverpool, UK

    August 20-24 Analysis and Singularities (Vladimir Arnol'd 70 year), Moscow, Russia

Text of the Research Proposal

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Related NWO- Russia project: 
Geometry and Singularity Theory in Mathematical Physics