Projekty a granty

Databáze všech projektů a grantů od roku 2010

LIE-DIFF-GEOM? Lie groups, differential equations and geometry
Id projektuIRSES 317721
Hlavní řešitelprof. RNDr. Olga Rossi, DrSc.
Období1/2013 - 7/2016
PoskytovatelRámcové programy EU
AnotaceThe main objective of the proposal is the creation, and development of a cooperative research network which utilizes thestrengths and synergies of the knowledge of the member research groups. This new cooperation symbolizes the coercivepower of two branches of mathematics, namely those of ALGEBRA and GEOMETRY, which had been unified first in thecreation Decartesian coordinate geometry. 3 of 6 research groups are on the edge of algebraic research, while the othersgained essential results and knowledge in geometry. With different backgrounds, new synergies and methodologies will ariseand accelerate the research activities.Besides the traditional mobility schemes and distributing ideas on conferences and publications, new methodology ofcontinuous reaction is planned to put in practice by the usage of world wide web, creating the platform of online webworkshops at regular times. This will ensure sustainability of the network for long time.We plan to achieve new scientific results on the following topics:? imprimitive transformation groups, affine geometries over paradual near rings;? fundamental theorem of geometric algebra, Novikov?s conjecture and the properties of skew-symmetric and symmetricelements for general involutions in group algebras.? multiplication loops of locally compact topological translation planes; Lie groups which are the groups topologicallygenerated by all left and right translations of topological loops;? the inverse problem of the calculus of variations for second order ordinary differential equations: existence of variationalmultipliers, in particular, of multipliers satisfying the Finsler homogeneity conditions, and Riemannian and Finsler metrizability;? metric structures associated with Lagrangians and Finsler functions? variational structures in Finsler geometry and applications in physics (general relativity, Feynmam integral);? Hamiltonian structures for homogeneous Lagrangians.