Objective The GALA is an Adventure STREP that will pioneer explorative instruments of mathematical geometric analysis in Lie groups and will provide on solid analytic basis novel modellistic tools for applications to vision and hearing and to magnetic resonance tomography. Sub Riemannian geometric analysis in Lie groups is an innovative field of scientific research, which considers the description of strongly non- isotropic systems.In particular it models the motion of a system in which some directions are not allowed by a constraint that is not necessarily a physical constraint, but that can be a differential one e.g. a magnetic field. The allowed directions of motion are called horizontal directions and are described through vector fields. These vector fields play t he role of derivatives in classical calculus all the theorems of analysis and differential geometry have to be rephrased in terms of these new instruments. We will need to define from a purely mathematical point of view, the main properties of the objects of the space, with instruments of Sub-Riemannian differential geometry, anisotropic partial differential equations of sub-elliptic and ultra-parabolic type and geometric measure theory in Lie groups. Results in this field will allow facing long- standing o pen problems in mathematics, which cannot be dealt with standard instruments. We will see that these instruments can be used to formalize models of the functional geometry of the cortex, and in particular to describe vision and hearing.Magnetic MRI induces rotation in the spin of the atoms and will be described in the Lie group of rotations. Quasi-linear mapping will describe composite media in material science. Finally we will need to develop numerical instruments in this anysotropic setting, in order to validate our results. The interaction within an interdisciplinary team will help in individuate the geometrical and analytic aspects more suited for the description of the different problems. Fields of science natural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) FP6-POLICIES - Policy support: Specific activities covering wider field of research under the Focusing and Integrating Community Research programme 2002-2006. Topic(s) POLICIES - Supporting policies and anticipating scientific and technological needs NEST-2004-ADV - Adventure activities Call for proposal FP6-2004-NEST-C-1 See other projects for this call Funding Scheme STREP - Specific Targeted Research Project Coordinator ALMA MATER STUDIORUM - UNIVERSITÀ DI BOLOGNA Address Via zamboni 33 Bologna Italy See on map Links Website Opens in new window EU contribution € 0,00 Participants (7) Sort alphabetically Sort by EU Contribution Expand all Collapse all HELSINGIN YLIOPISTO Finland EU contribution € 0,00 Address Yliopistonkatu 4 Helsingin yliopisto, helsinki See on map Links Website Opens in new window UNIVERSITAET SIEGEN Germany EU contribution € 0,00 Address Walter-flex-strasse 3 Siegen See on map Links Website Opens in new window NORGES TEKNISK NATURVITENSKAPELIGE UNIVERSITET Norway EU contribution € 0,00 Address Hogskoleringen 1 Trondheim See on map Links Website Opens in new window SOBOLEV INSTITUTE OF MATHEMATICS SIBERIAN BRANCH OF RUSSIAN ACADEMY OF SCIENCES Russia EU contribution € 0,00 Address Pr t academika koptyuga 4 Novosibirsk See on map Links Website Opens in new window UNIVERSITA DEGLI STUDI DI TRENTO Italy EU contribution € 0,00 Address Via belenzani 12 Trento See on map UNIVERSITY OF JYVÄSKYLÄ Finland EU contribution € 0,00 Address Seminaarinkatu 15 Jyväskylä See on map Links Website Opens in new window UNIVERSITÄT BERN Switzerland EU contribution € 0,00 Address Hochschulstrasse 4 Bern See on map Links Website Opens in new window
