Objectif The research topic of the proposal is Quantum Topology. This mathematical theory (which involves topology, algebra, and mathematical physics) was born in the 1990's and was inspired by the works of Jones, Witten, Drinfeld, Atiyah, Reshetikhin, Turaev, Kontsevich, and their followers. Structures which originally do not have any relation with topology (such as quantum groups, braided categories) appear of crucial importance in the construction of new topological invariants of knots, of 3-dimensional manifolds, and of fibre bundles over 3-manifolds. These non-classical "quantum" invariants belong to the general framework of topological/homotopical quantum field theories (T/HQFT). I propose a research project, which is directed according to four major objectives. These objectives are the natural extensions of as well my PhD thesis and actual research as the recent works of the scientific supervisors of the project who are Reshetikhin (at UC Berkeley) and Benedetti (at Pisa).More precisely, during the outgoing phase at the Department of Mathematics at Berkeley (United-States), I plan to acquire new competencies quantum group theory, representation theory, and 4-dimensional topology in order to:1) construct non-semi-simple TQFT via "Kirby elements";2) explore the implications of the "graded quantum groups" (that I have recently defined) into the topology of flat fibre bundles over 3-manifolds;3) construct the first non-trivial examples of 4-dimensional HQFT. During the return phase at the Department of Mathematics at Pisa, I plan to acquire new competencies in geometric and hyperbolic topology in order to:4) construct new quantum invariants of fibre bundles endowed with a (not necessarily) flat connection.The proposed mobility will allow me to pursue dynamic research by actively training and collaborating with world experts in famous mathematical centres. It appears to be a major step towards my professional independence as a researcher. Champ scientifique natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicspure mathematicstopologynatural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesmathematicspure mathematicsalgebra Mots‑clés Hopf algebras Low-dimensional topology category theory homotopy theory quantum groups quantum topology Programme(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Thème(s) MOBILITY-2.2 - Marie Curie Outgoing International Fellowships (OIF) Appel à propositions FP6-2002-MOBILITY-6 Voir d’autres projets de cet appel Régime de financement OIF - Marie Curie actions-Outgoing International Fellowships Coordinateur UNIVERSITÃ'Â DI PISA Contribution de l’UE Aucune donnée Adresse Lungarno Pacinotti n. 43 PISA Italie Voir sur la carte Liens Site web Opens in new window Coût total Aucune donnée Participants (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire DEPARTMENT OF MATHEMATICS, UNIVERSITY OF CALIFORNIA, BERKELEY États-Unis Contribution de l’UE Aucune donnée Adresse 970 Evans Hall #3840 BERKELEY Voir sur la carte Liens Site web Opens in new window Coût total Aucune donnée
