Wheeld props, differential geometry and quantum field theory

Project funded by Swedish Research Council (Project grant), grant 2008-05065_VR. Participating organisations named by the source: Stockholm University. Funded amount: SEK 1,842,000, as stated by the source. Runs 2009-01-01 to 2011-12-31. Keywords: Oklassificerat, Unclassified. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-06); national funding data, not CORDIS. Abstract given by the source: The theory of operads and props has undergone an explosive development in recent years in the sense of both the number of research publications and the variety of questions which are effectively approached with the help of this theory. Operads and props can be seen almost everywhere nowadays --- in algebraic topology, in homological algebra, in classical differential geometry, in non-commutative geometry, in string topology, in deformation theory, in quantization theory, in theoretical computer sciences. The theory is now developing into a kind of universal language in which mathematicians from, historically, different branches of mathematics can effectively and fruitfully communicate with each other. Our project aims to develop Koszul duality for quadratic wheeled properads and apply the results to the homotopy theory of bialgebras, computation of homology of several important graph complexes, deformation quantization of unimodular Poisson structures, and homotopy theory of Batalin-Vilkovisky manifolds. Our plans include a study of the new quantum simplicial BF theory for unimodular Lie 1-bialgebras and subsequent application of the Batalin quantization machinery for computing homotopy transfer formulae of certain quadratic wheeled props which control Poisson and Nijenhuis geometries. In particular, we want to give a new properadic meaning to the famous Feynman integrals in the theoretical physics, and hence develop new methods for regularizing and computing them.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Swedish Research Council. Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The project "Wheeld props, differential geometry and quantum field theory" was funded by the Swedish Research Council with a grant of SEK 1,842,000, running from January 1, 2009, to December 31, 2011, at Stockholm University. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.