VARIOGEO
The Geometric Calculus of Variations and its Applications
| Coordinatore | MAX PLANCK GESELLSCHAFT ZUR FOERDERUNG DER WISSENSCHAFTEN E.V.
Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie. |
| Nazionalità Coordinatore | Germany [DE] |
| Totale costo | 1˙500˙000 € |
| EC contributo | 1˙500˙000 € |
| Programma | FP7-IDEAS-ERC
Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | ERC-2010-AdG_20100224 |
| Funding Scheme | ERC-AG |
| Anno di inizio | 2011 |
| Periodo (anno-mese-giorno) | 2011-04-01 - 2016-03-31 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
MAX PLANCK GESELLSCHAFT ZUR FOERDERUNG DER WISSENSCHAFTEN E.V.
Organization address
address: Hofgartenstrasse 8 contact info |
DE (MUENCHEN) | hostInstitution | 1˙500˙000.00 |
| 2 |
MAX PLANCK GESELLSCHAFT ZUR FOERDERUNG DER WISSENSCHAFTEN E.V.
Organization address
address: Hofgartenstrasse 8 contact info |
DE (MUENCHEN) | hostInstitution | 1˙500˙000.00 |
Mappa
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Obiettivo del progetto (Objective)
'The project is concerned with the geometric calculus of variations and its applications in a wide range of fields. I start with fundamental examples of variational problems from geometry and physics, the Bernstein problem for minimal submanifolds of Euclidean spaces, non-abelian Hodge theory as a harmonic map approach to representations of Kähler groups, and Dirac harmonic maps as a mathematical version of the nonlinear supersymmetric sigma model of quantum field theory. These examples will motivate a general regularity and rigidity theory in geometric analysis that will be based in a fundamental way on convexity properties. Convexity will then be linked to concepts of non-positive curvature in geometry, and it will lead me to a general theory of duality relations and convexity. That theory will encompass the formal structures of the new calculus of variations and statistical mechanics, information theory and statistics, and mathematical population genetics in biology. Also, the connection with symmetry principles as arising in high energy theoretical physics will be systematically explored. Further applications lie in material sciences, pattern recognition, and bioinformatics. The project will thus achieve a novel integration of different disciplines from mathematics and the natural sciences.'