Synchrony in coupled systems: a connection between graphs and singularities
BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability
Classical-quantum mechanical systems symmetric by the action of a Lie group
Grant number: | 05/04558-0 |
Support type: | Research Projects - Thematic Grants |
Duration: | November 01, 2006 - October 31, 2011 |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
Principal researcher: | Alcibiades Rigas |
Grantee: | Alcibiades Rigas |
Home Institution: | Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil |
Pesquisadores principais: | Carlos Eduardo Duran Fernandez ; Marcos Benevenuto Jardim |
Assoc. researchers: | Adriano Adrega de Moura ; Ricardo Antonio Mosna |
Associated grant(s): | 09/12576-9 - Geometry of hyperkähler structures, AV.EXT |
Associated scholarship(s): | 09/10067-0 - Instantons over G2-manifolds,
BP.PD 09/07953-8 - Geometry and Topology of Coboundaries, BP.DR 09/05136-2 - Parabolic Higgs bundles on curves, BP.PD + associated scholarships - associated scholarships |
Abstract
The main theme of the proposal is the study of the various ways the concept of symmetry appears in algebra, geometry, topology and mathematical physics through a) actions of groups and algebras b) in its infinitesimal version, where the study of symmetries is encoded in representations of algebras, and c) in the study of deformations of algebraic structures and of group actions. As an example, we consider the study of exotic structures on manifolds, where the symmetries appear through exotic actions of groups and global properties of geodesics and of connections on principal fiber bundles with maximal symmetry. This path leads us to the study of special geometric structures relevant to mathematical physics. (AU)
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