Objective The aim of this project is to develop and apply efficient mathematical tools for studying quantum and classical phenomena in a discrete setting. The motivation is on one hand that on the fundamental level it seems that space-time is discrete, because of the existence of the Planck length and its role e.g. in quantum gravity. On the other hand, even in a continuous world many important phenomena are discrete, such as phenomena occurring in crystals or in molecular or atomic chains. Thus difference equations may be more fundamental than differential ones. Moreover, differential equations often have to be solved numerically and that means that they have to be discretized, i.e. approximated by a difference system.Our main interest is in models that can be solved exactly because of their symmetry and integrability properties. Of special interest are finite and infinite dimensional integrable and superintegrable models. Integrable systems have as many commuting integrals of motion as degrees of freedom (which may be infinite). Superintegrable systems have more integrals of motion than degrees of freedom and these integrals form interesting non-Abelian algebras. The integrals of motion are related to symmetries of the system. These may be Lie point symmetries but usually they are generalized symmetries and they form more general algebras than Lie ones. Our aim is to study and use Lie symmetries of difference equations and to discretize differential equations preserving their most important properties. These include their Lie point symmetries, generalized symmetries, integrability and superintegrability.In order to do so we plan to host a top-class researcher from a Canadian first class laboratory who is a founder and an expert in the field of symmetry preserving discretization and construction of superintegrable systems. This will strengthen the host institution’s research skills and its relations with the laboratory of the researcher. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationsnatural sciencesmathematicspure mathematicsalgebranatural sciencesphysical sciencestheoretical physics 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-2013-IIF - Marie Curie Action: "International Incoming Fellowships" Call for proposal FP7-PEOPLE-2013-IIF See other projects for this call Funding Scheme MC-IIF - International Incoming Fellowships (IIF) Coordinator UNIVERSITA DEGLI STUDI ROMA TRE EU contribution € 145 391,63 Address VIA OSTIENSE 133 00154 Roma Italy See on map Region Centro (IT) Lazio Roma Activity type Higher or Secondary Education Establishments Administrative Contact Virgilio Lo Presti (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
