Geometry of Grassmannian Lagrangian manifolds and their submanifolds, with applications to nonlinear partial differential equations of physical interest

Información del proyecto

GEOGRAL

Identificador del acuerdo de subvención: 654721

DOI

10.3030/654721

Proyecto cerrado

Fecha de la firma de la CE 18 Marzo 2015

Fecha de inicio 1 Septiembre 2015

Fecha de finalización 31 Agosto 2017

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 146 462,40

Aportación de la UE

€ 146 462,40

Coordinado por

INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK
Poland

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 (EuroSciVoc)

• ciencias naturales › matemáticas › matemáticas puras › álgebra
• ciencias naturales › matemáticas › matemáticas puras › geometría
• ciencias naturales › matemáticas › matemáticas puras › análisis matemático › ecuaciones diferenciales › ecuaciones diferenciales parciales
• ciencias naturales › informática y ciencias de la información › inteligencia artificial › programación heurística

Programa(s)

• H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions PROGRAMA PRINCIPAL
  
• 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)
  

Régimen de financiación

MSCA-IF-EF-ST - Standard EF

Convocatoria de propuestas

H2020-MSCA-IF-2014

Coordinador

INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK

• Aportación neta de la UEn: € 146 462,40
• Dirección: UL. SNIADECKICH 8 ; 00-656 Warszawa ; Polonia
• Pyme Sí:
  Región
  Makroregion województwo mazowieckie › Warszawski stołeczny › Miasto Warszawa
• Región: Makroregion województwo mazowieckie › Warszawski stołeczny › Miasto Warszawa
• Tipo de actividad: Higher or Secondary Education Establishments
• Coste total: € 146 462,40