Objetivo The aim of GEOGRAL is to strengthen the bonds of the geometric theory of nonlinear PDEs (and, in particular, integrable systems and equations of Monge-Ampère type) with the geometry of Lagrangian Grassmannians and their submanifolds. In spite of the evident parallelism between these two disciplines, attempts have been rare, yet sophisticated, to cast a bridge between them, and the Applicant himself already gave his own contribution in this direction: he clarified the structure of the space of non-maximal integral elements of the contact planes in jet spaces and studied 3rd order Monge-Ampère equations (which turn out to be of key relevance in topological field theories) through the so-called meta-symplectic structure on the 1st prolongation of a contact manifold.GEOGRAL has a wide applicative scope, as its theoretical results can be tested on equations and variational problems of key importance for Natural Sciences, Technology and Economy. Tailored to the Applicant's scientific profile and designed in continuity with his previous and current research activities, GEOGRAL consists of four research lines:[MOV] Regard Lagrangian Grassmannians as homogeneous spaces and and use Cartan's method of moving frame to classify their submanifolds, as in D. The's work, and characterise the corresponding invariant equations, in continuity with D. Alekseevsky's work.[HYD] Continue the study of certain rational normal curve bundles on Lagrangian Grassmannians, and their bisecant varieties, which are associated with integrable systems of hydrodynamic type, discovered by E. Ferapontov.[HMA] Geometric study of multi-dimensional and higher-order Monge-Ampère equations, initiated by G. Manno and the Applicant.[FBV] Study some examples of Cauchy problems and variational problems with free boundary values by exploiting the geometric structures on the spaces of isotropic flags and non-maximal isotropic elements of a meta-symplectic space, in continuity with the Applicant's own work. Ámbito científico natural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencescomputer and information sciencesartificial intelligenceheuristic programming Programa(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Tema(s) MSCA-IF-2014-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Convocatoria de propuestas H2020-MSCA-IF-2014 Consulte otros proyectos de esta convocatoria Régimen de financiación MSCA-IF-EF-ST - Standard EF Coordinador INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK Aportación neta de la UEn € 146 462,40 Dirección UL. SNIADECKICH 8 00-656 WARSZAWA Polonia Ver en el mapa Pyme Organización definida por ella misma como pequeña y mediana empresa (pyme) en el momento de la firma del acuerdo de subvención. Sí Región Makroregion województwo mazowieckie Warszawski stołeczny Miasto Warszawa Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 146 462,40
