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A graph complex valued field theory

Total Cost €


EC-Contrib. €






Project "GRAPHCPX" data sheet

The following table provides information about the project.


Organization address
address: Raemistrasse 101
postcode: 8092

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Switzerland [CH]
 Total cost 1˙162˙500 €
 EC max contribution 1˙162˙500 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-07-01   to  2021-06-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project 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.


year authors and title journal last update
List of publications.
2018 Najib Idrissi
The Lambrechts–Stanley model of configuration spaces
published pages: , ISSN: 0020-9910, DOI: 10.1007/s00222-018-0842-9
Inventiones mathematicae 2019-04-19
2018 Benoit Fresse, Victor Turchin, Thomas Willwacher
The homotopy theory of operad subcategories
published pages: 689-702, ISSN: 2193-8407, DOI: 10.1007/s40062-018-0198-2
Journal of Homotopy and Related Structures 13/4 2019-04-19
2018 Victor Turchin, Thomas Willwacher
Relative (non-)formality of the little cubes operads and the algebraic Cerf lemma
published pages: 277-316, ISSN: 1080-6377, DOI: 10.1353/ajm.2018.0006
American Journal of Mathematics 140/2 2019-04-19

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The information about "GRAPHCPX" are provided by the European Opendata Portal: CORDIS opendata.

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