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New methods and interacions in Singularity Theory and beyond

Objective

"This project is centred in Singularity Theory and its interactions and applications to Complex and Algebraic Geometry, Differential/symplectic/Contact Topology, Hodge Theory and Algebraic Topology. This subject is still at the core of various developments (Mori's Theory, Symplectic and Contact Geometry, algebro-geometric Donaldson-Thomas Theory, Hodge Theory and D-modules,...) In the present project we propose several directions of development in singularity theory, designed in order to approach the solution of several classical conjectures, and explore new interactions with the latest developments in nearby areas. New problems and conjectures are formulated, which are interesting bottlenecks whose solution would open new development perspectives in the theory, and whose study will need significantly new ideas. We have taken care of finding feasible starting points and interesting classes of singularities where the initial development is less steep. And to find links among the seemingly difernt techniques and problems which we propose.
We deal with the following specific topics: vanishing cohomology of isolated and non-isolated singularities. Rational homotopy generalisations of Hodge Theory and rational vanishing homotopy. Applications to Equisingularity questions. Disentanglement theory and its relation with vanishing homology and homotopy. Symplectic and contact geometry of milnor fibrations. A vast programme in topological equisingularity including a multifaceted attack to Lê-Ramanujan problem. Generalisations of McKay correspondence. Banagl Intersection spaces. Topological and analytic invariants of normal surface singularities. Arc spaces and Nash correspondence. Compactified Jacobians."

Field of science

  • /natural sciences/mathematics/pure mathematics/geometry
  • /natural sciences/mathematics/pure mathematics/topology/algebraic topology
  • /natural sciences/mathematics/pure mathematics/algebra/algebraic geometry

Call for proposal

ERC-2013-CoG
See other projects for this call

Funding Scheme

ERC-CG - ERC Consolidator Grants

Host institution

BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS
Address
Al Mazarredo 14
48009 Bilbao
Spain
Activity type
Research Organisations
EU contribution
€ 1 056 931
Principal investigator
Javier Jose Fernandez De Bobadilla De Olazabal (Dr.)
Administrative Contact
Miguel Angel Benitez Lozano (Mr.)

Beneficiaries (2)

BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS
Spain
EU contribution
€ 1 056 931
Address
Al Mazarredo 14
48009 Bilbao
Activity type
Research Organisations
Principal investigator
Javier Jose Fernandez De Bobadilla De Olazabal (Dr.)
Administrative Contact
Miguel Angel Benitez Lozano (Mr.)
AGENCIA ESTATAL CONSEJO SUPERIOR DEINVESTIGACIONES CIENTIFICAS

Participation ended

Spain
EU contribution
€ 83 670
Address
Calle Serrano 117
28006 Madrid
Activity type
Research Organisations
Administrative Contact
Guillermo Sanjuanbenito (Mr.)