GRAPHCPX
Financiado
A graph complex valued field theory
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,...
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.
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Duración del proyecto: 63 meses
Fecha Inicio: 2016-03-01
Fecha Fin: 2021-06-30
Fecha Fin: 2021-06-30
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2021-06-30
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-StG-2015:
ERC Starting Grant
Cerrada
hace 9 años
Presupuesto
El presupuesto total del proyecto asciende a
1M€
Líder del proyecto
EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
No se ha especificado una descripción o un objeto social para esta compañía.
161.78K€ |
Participante