Graphic summary
  • Show / hide key
  • Information


Scientific and technological production
  •  

1 to 48 of 48 results
  • Integrable systems and group actions

     Miranda Galceran, Eva
    Central european journal of mathematics
    Date of publication: 2014
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    The main purpose of this paper is to present in a unified approach to different results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective.

  • On a Poincaré Lemma for Foliations

     Miranda Galceran, Eva; Solha, Romero
    Date of publication: 2013
    Book chapter

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    The following sections are included: Introduction / Singular foliations given by nondegenerate integrable systems / A singular Poincaré lemma for a deformation complex / Homotopy operators and a regular Poincaré lemma for foliated cohomology Foliated cohomology / Geometric Quantization à la Kostant / The singular case / Singular foliated cohomology / Analytical tools: special decomposition of smooth functions / Computation of foliated cohomology groups / References Read More: http://www.worldscientific.com/doi/abs/10.1142/9789814556866_0007?prevSearch=%5BPubIdSpan%3A+%2210.1142%2F9789814556866_0007%22%5D&searchHistoryKey=

  • Coupling symmetries with Poisson structures

     Miranda Galceran, Eva; Laurent Gengoux, Camille
    Acta Mathematica Vietnamica
    Date of publication: 2013
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Preface Special Issue: GESTA 2011: New Trends in Symplectic and Contact Geometry

     Miranda Galceran, Eva; Garcia Prada, Oscar; Ginzburg, Viktor; Goldman, William; Muñoz Velázquez, Vicente
    Geometricae dedicata
    Date of publication: 2013
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • A Poincaré lemma in geometric quantisation

     Miranda Galceran, Eva; Solha, Romero
    Journal of Geometric Mechanics
    Date of publication: 2013-12
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    This article presents a Poincaré lemma for the Kostant complex, used to compute geometric quantisation, when the polarisation is given by a Lagrangian foliation defined by an integrable system with nondegenerate singularities

  • On geometric quantisation of integrable systems with singularities

     Barbieri Solha, Romero
    Defense's date: 2013-10-21
    Universitat Politècnica de Catalunya
    Theses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • GEOMATRIA ALGEBRAICA, SIMPLECTICA, ARITMETICA Y APLICACIONES

     Alberich Carramiñana, Maria; Amoros Torrent, Jaume; Barja Yañez, Miguel Angel; Elgueta Montó, Josep; Fernández Sánchez, Jesús; Ventura González Alonso, Daniel; Barbieri Solha, Romero; Miranda Galceran, Eva; Pascual Gainza, Pedro; Roig Marti, Agustin; Roig Maranges, Abdo; Feliu Trijueque, Elsienda; Gálvez Carrillo, Maria Immaculada; Casanellas Rius, Marta
    Participation in a competitive project

     Share

  • Research programme on Geometry and Dynamics of Integrable Systems

     Miranda Galceran, Eva
    Participation in a competitive project

     Share

  • Geometry and Dynamics of Integrable Systems

     Miranda Galceran, Eva
    Collaboration in exhibitions

     Share

  • Access to the full text
    From b-Poisson manifolds to symplectic mapping tori and back  Open access

     Miranda Galceran, Eva; Guillemin, Victor; Pissarra Pires, Ana Rita
    Thematic Day on Poisson Geometry and Applications
    Presentation's date: 2012
    Presentation of work at congresses

    Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

  • The Hirsch conjecture has been disproved : an interview with Francisco Santos

     Miranda Galceran, Eva
    Newsletter of the European Mathematical Society
    Date of publication: 2012-12-01
    Journal article

     Share Reference managers Reference managers Open in new window

  • Monodromías Geométricas en Familias de Curvas de Género 4  Open access

     Berna Sepulveda, Isabel Silvana
    Defense's date: 2012-02-10
    Department of Applied Mathematics I, Universitat Politècnica de Catalunya
    Theses

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    The goal of the thesis is the effective computation of the geometric monodromy, equivalently the monodromy in the fundamental group, for families of compact connected Riemann surfaces (complex algebraic curves) of genus 4. This extends previous work up to genus 2, by using the trigonal structure (triple cover of the Riemann sphere) of genus 4 curves: they have 2 such structures, so a 2:1 base change for any family of them allows the glueing of the trigonal structures to form a family of trigonal covers of the Riemann sphere. The generic trigonal genus 4 covering has branching in 12 simple points. In a family of trigonal covers these form a branching divisor of relative degree 12, whose braid monodromy determines the geometric monodromy of the family. The main theoretic result of the thesis is the construction of a universal family of trigonal genus 4 curves, inside the Hurwitz scheme of trigonal covers but with a lower dimension, computable geometric monodromy, and with a topological universality property: any family of trigonal genus 4 curves is obtained from this universal family by pullback plus deformation of a map to its base. This theorem is completed with the computation of the monodromy in the fundamental group for this universal family. The computation is derived from the braid monodromy of the branching divisor, which is then lifted to the trigonal covers. A gap remains in the computation of the monodromy for this universal family: it is a conjecture about the stabilizer of a braid group action on the Hurwitz scheme that remains open. If the conjecture is true then the computed geometric monodromy is that of the universal trigonal family. If the conjecture is false the monodromy computations in the thesis remain valid, but have to be completed with analogous computations to cover all the universal family. The theoretical results in the thesis are completed with effective computation tools for them. A library of functions for the program Singular is developed, to find the trigonal structure of genus 4 curves from their canonical equation, and with help of a Pari-GP procedure, to find the equation of the branching divisor in a family of canonical genus 4 curves. This library is applied to examples of geometric interest: - the Lefschetz pencil of hyperplane sections in the genus 4 projective K3 surface (whose geometric monodromy is necessary to prove Seidel¿s version of the Mirror Symmetry conjecture on these surfaces). - a 1-parameter deformation of the Bring curve. Moreover, a library of functions for the program Matlab is developed, in order to compute the braid monodromy of a divisor in C^2. It is based on the integration of a system of complex-valued ordinary differential equations which determines the branches of the divisor. This is done with a Runge-Kutta method with variable step size regulated by the equation of the divisor, used as a first integral. The ode system is integrated over a path system formed by the boundaries of the Voronoi cells of the branching values of the divisor. The braid monodromy is then determined from the evolution of the branches of the divisor along this path system. This library is successfully applied to compute the braid monodromy of academic examples of degrees 6-8 in the thesis.

    El objetivo de la tesis es el calculo efectivo de la monodromía geométrica y en el grupo fundamental, de familias de superficies de Riemann compactas conexas (curvas algebraicas complejas) de género 4. Este estudio se extiende a otros desarrollados hasta la fecha en los marcos de la Geometría Algebraica, Topología Diferencial y Simpléctica, que estudian esta monodromía geométrica y en el grupo fundamental para familias de superficies de Riemann de hasta género 2, usando la estructura elíptica/hiperelíptica de tales familias. El salto de género 2 a género 4 se realiza para aprovechar la estructura trigonal (de recubrimiento triple de la esfera de Riemann) que tienen las curvas en género 4. Tal curva genérica tiene dos estructuras trigonales, en una familia genérica se puede hacer un cambio de base 2:1 para conseguir pegar las estructuras de recubrimiento trigonal de las fibras y obtener una familia de recubrimientos trigonales de la esfera de Riemann. El recubrimiento trigonal genérico para curvas de género 4 tiene 12 puntos de ramificación simple. Esto significa, en una familia de recubrimientos trigonales hay un divisor de grado relativo 12 en la familia de esferas de Riemann recubiertas, denominado divisor de ramificación, tal que la monodromía de trenzas de este divisor determina la monodromía geométrica y en el grupo fundamental de la familia. El resultado teórico principal de esta memoria es la construcción de una familia universal de curvas trigonales de género 4, bajo el esquema de recubrimientos trigonales de Hurwitz, pero de dimensión más reducida, monodromía geométrica calculable, y que mantiene una propiedad de universalidad topológica: toda familia de recubrimientos trigonales de género 4 se obtiene por pullback de una aplicación de la base a la de esta familia universal, más deformación. Completa el resultado teórico principal el cálculo de la monodromía geométrica y en el grupo fundamental de esta familia. Este cálculo se hace siguiendo la monodromía de trenzas del divisor de ramificación de la familia, y levantando esta monodromía de las esferas de Riemann a sus cubiertas triples. El cálculo de la monodromía en el grupo fundamental de la familia no ha podido ser completado desde el punto de vista lógico, debido a una conjetura sobre el estabilizador de una acción del grupo de trenzas en el esquema de Hurwitz de cubiertas triples. Sin embargo, los cálculos realizados permanecen válidos sea cual sea la respuesta; en caso de ser cierta implica que el cálculo realizado es toda la monodromía de la familia universal y lo contrario significaría que hay que añadir algunos cálculos de monodromía análogos a los aquí realizados. Los resultados teóricos de la tesis se completan con trabajo de computación para realizar cálculos efectivos de monodromía geométrica en el grupo fundamental en las familias de curvas de género 4. Primero, se desarrolla una librería de funciones para el programa Singular que hallan la estructura trigonal de curvas de género 4 a partir de su ecuación canónica y con la ayuda de un cálculo auxiliar en Pari-GP, determinan el divisor de ramificación relativo de una familia de curvas de género 4 canónicas (no hiperelípticas). En la tesis se aplica esta librería al cálculo de estructuras trigonales y divisores de ramificación en familias de curvas de género 4, tanto ejemplos académicos como familias de interés geométrico: - la familia de curvas de género 4 que describe un pincel de Lefschetz en la superficie K3 de género 4 (cuya monodromía geométrica es necesaria para demostrar la versión de Paul Seidel de la conjetura de la 'Mirror Symmetry'), - una familia de curvas de género 4 deformación de la curva de Bring (la única curva de género 4 que tiene grupo de simetrías de orden 5). Segundo, se desarrolla una librería de funciones para el programa MATLAB que calculan la monodromía de trenzas de un divisor en C^2. Este cálculo se inicia en la integración de un sistema de ecuaciones diferenciales ordinarias a valores complejos, que sigue la evolución de las ramas del divisor, para el que se ha desarrollado un integrador numérico de paso variable combinando un método de Runge-Kutta con el uso de la ecuación del divisor como integral primera de las soluciones para el control del paso. Este sistema de ecuaciones se integra sobre un sistema de generadores del grupo fundamental de la base obtenido a partir de una descomposición celular de Voronoi asociada a los valores de ramificación de la familia, y finalmente se identifica la monodromía de trenzas a partir del análisis de la posición de las ramas del divisor a lo largo de los caminos escogidos en la base. Esta librería funciona correctamente para divisores de grados hasta 6-8 en el plano. Se ilustra en la tesis mediante su aplicación a ejemplos académicos, completa con representación e identificación de las monodromías de trenzas en estos ejemplos.

  • Internacional : la columna de l'EMS

     Miranda Galceran, Eva
    Date: 2012-03
    Report

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Access to the full text
    Symplectic and Poisson geometry on b-manifolds  Open access

     Guillemin, Victor; Miranda Galceran, Eva; Pissarra Pires, Ana Rita
    Date: 2012
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    Let M2n be a Poisson manifold with Poisson bivector field . We say thatM is b-Poisson if the map n : M ! 2n(TM) intersects the zero section transversally on a codimension one submanifold Z M. This paper will be a systematic investigation of such Poisson manifolds. In particular, we will study in detail the structure of (M, ) in the neighbourhood of Z and using symplectic techniques define topological invariants which determine the structure up to isomorphism. We also investigate a variant of de Rham theory for these manifolds and its connection with Poisson cohomology

  • Coupling symmetries with Poisson structures

     Laurent Gengoux, Camille; Miranda Galceran, Eva
    Date: 2012-10-30
    Report

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    In this paper we study normal forms problems for integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The equivariant normal forms are obtained at the local level. The existence of Weinstein’s splitting theorem for the integrable system is also studied giving some examples in which such a splitting cannot split. This splitting allows to decompose the integrable system locally as a product of an integrable system on the symplectic leaf and a symplectic leaf on the transversal. The problem of splitting for integrable systems with additional symmetries is also considered

  • From action-angle coordinates to geometric quantization: a round-trip

     Miranda Galceran, Eva
    Geometric Quantization in the non-compact setting
    Presentation's date: 2011
    Presentation of work at congresses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Geometric quantisation of integrable systems with nondegenerate singularities

     Miranda Galceran, Eva; Barbieri Solha, Romero
    Geometric Quantization in the non-compact setting
    Presentation's date: 2011
    Presentation of work at congresses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • From action-angle coordinates to geometric quantization: a round trip

     Miranda Galceran, Eva
    Oberwolfach reports
    Date of publication: 2011
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • GESTA2011: New Trends in Symplectic and Contact Geometry

     Miranda Galceran, Eva
    Participation in a competitive project

     Share

  • Access to the full text
    Integrable systems and group actions  Open access

     Miranda Galceran, Eva
    Date: 2011
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    The main purpose of this paper is to present in a uni¯ed approach to see di®erent results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective.

  • Access to the full text
    Rigidity of Hamiltonian actions on Poisson manifolds  Open access

     Miranda Galceran, Eva; Monnier, Philippe; Tien Zung, Nguyen
    Date: 2011-02-01
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    This paper is about the rigidity of compact group actions in the Poisson context. The main result is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash-Moser normal form theorem for closed subgroups of SCI-type. This Nash-Moser normal form has other applications to stability results that we will explore in a future paper. We also review some classical rigidity results for differentiable actions of compact Lie groups and export it to the case of symplectic actions of compact Lie groups on symplectic manifolds.

  • Codimension one symplectic foliations and regular Poisson structures

     Miranda Galceran, Eva; Guillemin, Victor; Pissarra Pires, Ana Rita
    Bulletin of the Brazilian Mathematical Society
    Date of publication: 2011
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Rigidity of hamiltonian actions on poisson manifolds

     Miranda Galceran, Eva; Tien Zung, Nguyen; Monnier, Philippe
    Advances in mathematics
    Date of publication: 2011-11-08
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • The Clay Public Lecture and Conference on the Poincaré Conjecture, Paris, 7-9 June 2010

     Miranda Galceran, Eva
    Newsletter of the European Mathematical Society
    Date of publication: 2010-09
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • I-MATH future

     Miranda Galceran, Eva; Suarez Serrato, Pablo
    Participation in a competitive project

     Share

  • Access to the full text
    Codimension one symplectic foliations and regular Poisson manifolds  Open access

     Guillemin, Victor; Miranda Galceran, Eva; Pissarra Pires, Ana Rita
    Date: 2010
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These manifolds and their regular Poisson structures admit an extension as the critical hypersurface of a b-Poisson manifold as we will see in [GMP].

  • Sheaf properties for the geometric quantization

     Miranda Galceran, Eva; Presas, Francisco
    Date: 2010
    Report

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Symplectic and Poisson geometry of b-manifolds

     Guillemin, Victor; Miranda Galceran, Eva; Pissarra Pires, Ana Rita
    Date: 2010
    Report

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Tranverse integrable systems

     Laurent Gengoux, Camille; Miranda Galceran, Eva
    Date: 2010
    Report

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Action-angle coordinates for integrable systems on Poisson manifolds

     Laurent Gengoux, Camille; Miranda Galceran, Eva; Vanhaecke, Pol
    International mathematics research papers
    Date of publication: 2010-07-13
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Geometric quantization of integrable systems with hyperbolic singularities

     Hamilton, Mark; Miranda Galceran, Eva
    Annales de l'Institut Fourier
    Date of publication: 2010-01-01
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Rigidity for Hamiltonian actions on Poisson manifolds

     Miranda Galceran, Eva; Tien Zung, Nguyen; Monnier, Philippe
    Date: 2009
    Report

     Share Reference managers Reference managers Open in new window

  • Access to the full text
    Symmetries and singularities in Hamiltonian systems  Open access

     Miranda Galceran, Eva
    Journal of physics: conference series
    Date of publication: 2009
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    This paper contains several results concerning the role of symmetries and singularities in the mathematical formulation of many physical systems. We concentrate in systems which nd their mathematical model on a symplectic or Poisson manifold and we present old and new results from a global perspective

  • Some rigidity results for symplectic and Poisson group actions

     Miranda Galceran, Eva
    International Workshop on Geometry and Physics
    Presentation's date: 2007
    Presentation of work at congresses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Rigidity for Poisson group actions

     Miranda Galceran, Eva
    Oberwolfach reports
    Date of publication: 2007
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    In this talk we ¯rst review some classical results of rigidity for group actions of compact Lie groups on smooth manifolds and then we prove some rigidity results in the case the group action preserves a Poisson structure. The details of these proofs can be found in the paper [11] and the preprint [10]. In the general case of actions of compact Lie groups on smooth manifold there are two well-known results that entail rigidity. The ¯rst one is the theorem of Bochner [1] that says that actions of compact Lie groups can be linearized in a neighbourhood of a ¯xed point for the action. The second one is the theorem of Palais [12], that establishes that C1-close actions of compact Lie groups are conjugated via a di®eomorphism close to the identity.

  • Some rigidity results for symplectic and Poisson group actions

     Miranda Galceran, Eva
    Publicaciones de la Real Sociedad Matemática Española
    Date of publication: 2007
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • A note on equivariant normal forms of Poisson structures

     Miranda Galceran, Eva; Tien Zung, Nguyen
    Mathematical research letters
    Date of publication: 2006-09
    Journal article

     Share Reference managers Reference managers Open in new window

  • A singular Poincaré lemma

     Miranda Galceran, Eva; Vu Ngoc, San
    International mathematics research notices
    Date of publication: 2005
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Access to the full text
    A normal form theorem for integrable systems on contact manifolds  Open access

     Miranda Galceran, Eva
    Publicaciones de la Real Sociedad Matemática Española
    Date of publication: 2005
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We present a normal form theorem for singular integrable systems on contact manifolds

  • Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems

     Miranda Galceran, Eva; Tien Zung, Nguyen
    Annales scientifiques de l'école normale supérieure
    Date of publication: 2004
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Symplectic linearization of singular Lagrangian foliations in M4

     Curras-Bosch, Carles; Miranda Galceran, Eva
    Differential geometry and its applications
    Date of publication: 2003-03
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    We prove that the singular Lagrangian foliation of a 2-degree of freedom integrable Hamiltonian system, is symplectically equivalent to the linearized foliation in a neighbourhood of a non-degenerate singular orbit.

  • On the symplectic classification of singular Lagrangian foliations

     Miranda Galceran, Eva
    Fall Workshop on Geometry and Physics
    Presentation's date: 2001
    Presentation of work at congresses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Foliaciones Lagrangianas

     Miranda Galceran, Eva
    Geometria Simpléctica con Técnicas Algebraicas 2000
    Presentation's date: 2000-02-17
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • Symplectic Linearization of singular Lagrangian Foliations

     Miranda Galceran, Eva
    IX Fall Workshop on Geometry and Physics
    Presentation's date: 2000-07-07
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • On the symplectic classification of singular Lagrangian foliations

     Miranda Galceran, Eva
    Publicaciones de la Real Sociedad Matemática Española
    Date of publication: 2000
    Journal article

     Share Reference managers Reference managers Open in new window

  • Integrabilidad de ecuaciones diferenciales en el plano

     Miranda Galceran, Eva; Jaume Giné (UdL), Dr
    Participation in a competitive project

     Share