Objectif The project has two fundamental aims: A) Open new research horizons exploiting the interplay between Operator Algebras and Conformal Quantum Field Theory. B) Use Operator Algebraic methods for a deeper understanding of the internal structure of Conformal Quantum Field Theory, with a possible feedback for Operator Algebras. A) concerns two points in particular: - Find Noncommutative Geometrical structures associated with certain representations of Conformal Nets of von Neumann algebras and provide index theorems for quantum systems with infinitely many degrees of freedom in this framework. - Set up relations between Vertex Algebras and Local Conformal Nets and so provide new methods and results in each of these two subjects by importing and developing methods of the other subject. B) concerns in particular the analysis of following points, some motivated by A): - Structure and classification of conformal nets of von Neumann algebras on the circle and on two-dimensional spacetimes, and of their representations; in particular conformal supersymmetric models. - KMS and super-KMS functional structure in conformal models. - Boundary Conformal Field Theory, in particular regarding new thermalization effects. - Conformal subnet structure, in particular restrictions on the possible index values for conformal subnets. - Nuclearity and trace class properties for representations and modularity properties. Champ scientifique natural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisoperator algebranatural sciencesmathematicsapplied mathematicsmathematical physicsconformal field theory Mots‑clés Field Quantum Quantum Field Theory Theory Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Appel à propositions ERC-2008-AdG Voir d’autres projets de cet appel Régime de financement ERC-AG - ERC Advanced Grant Institution d’accueil UNIVERSITA DEGLI STUDI DI ROMA TOR VERGATA Contribution de l’UE € 1 044 750,00 Adresse VIA CRACOVIA 50 00133 Roma Italie Voir sur la carte Région Centro (IT) Lazio Roma Type d’activité Higher or Secondary Education Establishments Contact administratif Giuseppe Novelli (Prof.) Chercheur principal Roberto Longo (Prof.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire UNIVERSITA DEGLI STUDI DI ROMA TOR VERGATA Italie Contribution de l’UE € 1 044 750,00 Adresse VIA CRACOVIA 50 00133 Roma Voir sur la carte Région Centro (IT) Lazio Roma Type d’activité Higher or Secondary Education Establishments Contact administratif Giuseppe Novelli (Prof.) Chercheur principal Roberto Longo (Prof.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée