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. Fields of science natural sciencesmathematicspure mathematicstopologyalgebraic topologynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-CG-2013-PE1 - ERC Consolidator Grant - Mathematics 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 EU contribution € 1 061 676,00 Address AL MAZARREDO 14 48009 Bilbao Spain See on map Region Noreste País Vasco Bizkaia Activity type Research Organisations Administrative Contact Miguel Angel Benitez Lozano (Mr.) Principal investigator Javier Jose Fernandez De Bobadilla De Olazabal (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (2) Sort alphabetically Sort by EU Contribution Expand all Collapse all BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS Spain EU contribution € 1 061 676,00 Address AL MAZARREDO 14 48009 Bilbao See on map Region Noreste País Vasco Bizkaia Activity type Research Organisations Administrative Contact Miguel Angel Benitez Lozano (Mr.) Principal investigator Javier Jose Fernandez De Bobadilla De Olazabal (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS Participation ended Spain EU contribution € 78 925,00 Address CALLE SERRANO 117 28006 Madrid See on map Region Comunidad de Madrid Comunidad de Madrid Madrid Activity type Research Organisations Administrative Contact Guillermo Sanjuanbenito (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data