Objective This project will be hosted at the MIT (outgoing host) and at the University of Zurich (returnhost). Its main objectives are :(I) to develop a theory of homotopy quantum groups. This can be understood as the natural the-ory that should sit at the intersection of four important disciplines of mathematics and physics :monoidal categories, homotopy theory, quantum groups and higher categories. This fact gives aclear multidisciplinary aspect to the proposal.(II) to prove the formality of the homotopy Lie algebra governing simultaneous deformations of aPoisson manifold and its coisotropic submanifolds. This is the key step in solving the problem ofquantization of symmetries from the point of view of deformation quantization, giving interdisciplinary applications. These two objectives organize themselves into subobjectives :I1 ) define homotopy braided monoidal categories (∞-braided ∞-monoidal category)I2 ) define homotopy quasi-triangular quasi-Hopf algebras (∞-triangular ∞-Hopf algebras)I3 ) define monodromy for higher connectionsI4 ) give examples of higher Drinfeld associatorsI5 ) define and give examples of homotopy quantum groupsII1 ) construct the homotopy Lie algebra governing simultaneous deformations of aPoisson manifold and its coisotropic submanifoldsII2 ) prove the formality of this homotopy Lie algebra.Interdisciplinary aspects come also from tools used which are borrowed from physics (higherholonomies, branes, quantization) or from new rewriting techniques in computer science and operads (Gröbner basis). Fields of science natural sciencesmathematicspure mathematicsalgebranatural sciencescomputer and information sciences Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) FP7-PEOPLE-2010-IOF - Marie Curie Action: "International Outgoing Fellowships for Career Development" Call for proposal FP7-PEOPLE-2010-IOF See other projects for this call Funding Scheme MC-IOF - International Outgoing Fellowships (IOF) Coordinator University of Zurich Address Ramistrasse 71 8006 Zurich Switzerland See on map Activity type Higher or Secondary Education Establishments Administrative Contact Alberto Cattaneo (Prof.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution No data
