Project description DEENESFRITPL A universal topological field theory with values in graph complexes Topology, historically a topic of mathematics, has gained critical practical value and significantly renewed interest with the discovery of topological materials and advances in accessing topological states of matter. The ERC-funded GRAPHCPX aims to create a universal topological field theory with values in graph complexes uniting areas of mathematical physics, topology, homological algebra, and algebraic geometry. It could provide: a precise topological interpretation of a class of well-studied topological field theories; new tools to study objects like configuration and embedding spaces and potentially diffeomorphism groups; and a wealth of new algebraic structures on graph complexes, some of the most important objects in the field. Show the project objective Hide the project objective Objective The goal of the proposed project is to create a universal (AKSZ type) topological field theory with values in graph complexes, capturing the rational homotopy types of manifolds, configuration and embedding spaces.If successful, such a theory will unite certain areas of mathematical physics, topology, homological algebra and algebraic geometry. More concretely, from the physical viewpoint it would give a precise topological interpretation of a class of well studied topological field theories, as opposed to the current state of the art, in which these theories are defined by giving formulae without guarantees on the non-triviality of the produced invariants. From the topological viewpoint such a theory will provide new tools to study much sought after objects like configuration and embedding spaces, and tentatively also diffeomorphism groups, through small combinatorial models given by Feynman diagrams. In particular, this will unite and extend existing graphical models of configuration and embedding spaces due to Kontsevich, Lambrechts, Volic, Arone, Turchin and others.From the homological algebra viewpoint a field theory as above provides a wealth of additional algebraic structures on the graph complexes, which are some of the most central and most mysterious objects in the field.Such algebraic structures are expected to yield constraints on the graph cohomology, as well as ways to construct series of previously unknown classes. Fields of science natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicspure mathematicstopologyalgebraic topologynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-StG-2015 - ERC Starting Grant Call for proposal ERC-2015-STG See other projects for this call Funding Scheme ERC-STG - Starting Grant Host institution EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH Net EU contribution € 1 162 500,00 Address Raemistrasse 101 8092 Zuerich Switzerland See on map Region Schweiz/Suisse/Svizzera Zürich Zürich Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 162 500,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH Switzerland Net EU contribution € 1 162 500,00 Address Raemistrasse 101 8092 Zuerich See on map Region Schweiz/Suisse/Svizzera Zürich Zürich Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 162 500,00
