Observatorio de I+D+i UPM

Memorias de investigación
Proyecto de I+D+i:
Geometría de Espacios Modulí
Año:2012
Áreas de investigación
  • Física química y matemáticas
Datos
Descripción
This project is devoted to the study of moduli spaces and their relation with various geometric structures. Moduli spaces are important because they are basic and central objects that emerge in the most natural classification problems in geometry. This importance has been emphasized over the years due to the relation of these spaces with areas of mathematics so diverse as algebraic geometry, differential geometry, topology, algebra, and, perhaps more surprisingly, with theoretical physics. Of particular interest in this project are the moduli spaces of holomorphic bundles equipped with additional structures of diverse types, among which are included vector bundles, principal bundles, Higgs bundles and coherent sheaves, as well as moduli spaces of solutions of equations of gauge type, and moduli spaces of representations of the fundamental groups of both Riemann surfaces and Kähler manifolds of higher dimension in a Lie group. The proposed objectives of the project are organized around the following fundamental aspects of the theory: construction of moduli spaces; Hitchin-Kobayashi correspondence; topology of moduli spaces; moduli spaces and algebro-geometric structures; moduli spaces and differential-geometric structures; and automorphisms, transformations, and dualities of moduli spaces. These are themes of great interest in the study of which there is much activity internationally. The threefold nature of the moduli spaces considered (topological, differential, and algebraic) reflects the rich geometry of these spaces and to a great extent explains the necessity of combining in the project techniques from differential geometry, algebraic geometric, algebra, algebraic topology, arithmetic geometry and global analysis.
Internacional
No
Tipo de proyecto
Proyectos y convenios en convocatorias públicas competitivas
Entidad financiadora
Ministerio de Ciencia e Innovación
Nacionalidad Entidad
ESPAÑA
Tamaño de la entidad
Desconocido
Fecha concesión
01/01/2011
Esta actividad pertenece a memorias de investigación
Participantes
  • Participante: Daniel Jeremy Fox Hornig (UPM)
  • Director: Oscar García Prada
  • Participante: Luis Álvarez Cónsul
  • Participante: Marina Logares Jiménez
  • Participante: Christian Pauly
  • Participante: Olivier Biquard
  • Participante: Alastair King
Grupos de investigación, Departamentos, Centros e Institutos de I+D+i relacionados
  • Creador: Departamento: Matemática Aplicada (E.U.I.T. Industrial)
S2i 2021 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)