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From Quantum Field Theory to Motives and 3-manifolds

Objectif

Quantization has been a potent source of interesting ideas in mathematics. This project aims to investigate a series of problems in pure mathematics, all having their roots and solutions in perturbative quantum field theory (pQFT). Below is a brief description of these subprojects.

* Motivic Renormalizations:
This project proposes to study motivic aspects of renormalization in order to understand number and homotopy theoretic properties of perturbative quantum field theories. The focal point of this project is to answer the main open problems of the field; explaining the presence of multiple zeta values and proving that pQFTs are indeed form E_d-algebras.

* Algebraization of 3-manifolds:
This project proposes a combinatorial reconstruction of 3-dimensional manifolds out of certain Feynman graphs and connections to bialgebras. This approach can be seen as a 3-dimensional generalization of the theory of Strebel differentials. It suggests a set of new invariants of 3-manifolds and their connection to the known ones (such Turaev-Viro, Reshetikhin-Turaev, finite type invariants). This combinatorial construction should also be related to a tensor model that is a generalization of Kontsevich’s matrix model in and such a model will be able to provide fundamental topological characteristics as Kontsevich’s model does in dimension two.

Champ scientifique (EuroSciVoc)

Programme(s)

Thème(s)

Appel à propositions

FP7-PEOPLE-2012-CIG
Voir d’autres projets de cet appel

Régime de financement

MC-CIG - Support for training and career development of researcher (CIG)

Coordinateur

UNIVERSITE DU LUXEMBOURG
Contribution de l’UE
€ 100 000,00
Adresse
2 PLACE DE L'UNIVERSITE
4365 ESCH-SUR-ALZETTE
Luxembourg
Région
Luxembourg Luxembourg Luxembourg
Type d’activité
Higher or Secondary Education Establishments
Liens
Coût total
Aucune donnée