Graphic summary
  • Show / hide key
  • Information


Scientific and technological production
  •  

1 to 50 of 112 results
  • Convexity for Hamiltonian torus actions on b-symplectic manifolds

     Guillemin, Victor; Miranda Galceran, Eva; Pires, Ana Rita; Scott, Geoffrey
    Date: 2014-12
    Report

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

    In [GMPS] we proved that the moment map image of a b-symplectic toric manifold is a convex b-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on b-symplectic manifolds. The modular weights of the action on the connected components of the exceptional hypersurface play a fundamental role: either they are all zero and the moment map behaves as in classic symplectic one, or they are all nonzero and the moment map behaves as in the toric b-symplectic case studied in [GMPS].

  • Random test examples with known minimum for convex semi-infinite programming problems

     Ferrer Biosca, Alberto; Miranda Galceran, Eva
    Workshop on Advances in Continuous Optimization
    p. 26
    Presentation's date: 2014-07-11
    Presentation of work at congresses

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

    A signifcant research activity has occurred in the area of convex semi-infinite optimization in the recent years. Many new theoretical, algorithm and computational contribution has been obtained. Despite these numerous contributions, there still exits a lack of representative convex semi-infinite test problems. This presentation is motivated by the scarcity of convex semi-infinite test problems and describes a procedure for generating convex semi-infnite families of test problems with optimal solution and optimal value known.

  • Access to the full text
    Rigidity of Poisson Lie group actions  Open access

     Miranda Galceran, Eva
    DOI: arxiv.org/abs/1410.5202v1
    Date: 2014
    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

    n this paper we prove that close infinitesimal momentum maps associated to Poisson Lie actions are equivalent under some mild assumptions. We also obtain rigidity theorems for actual momentum maps (when the acting Lie group G is endowed with an arbitrary Poisson structure) combining a rigidity result for canonical Hamiltonian actions (\cite{MMZ}) and a linearization theorem(\cite{GW}). These results have applications to quantization of symmetries since these infinitesimal momentum maps appear as the classical limit of quantum momentum maps (\cite{BEN}).

  • Symplectic and Poisson geometry on b-manifolds

     Miranda Galceran, Eva; Guillemin, Victor; Pires, Ana Rita
    Advances in mathematics
    Vol. 264, p. 864-896
    DOI: 10.1016/j.aim.2014.07.032
    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

    Let M2nM2n be a Poisson manifold with Poisson bivector field ¿ . We say that M is b -Poisson if the map ¿n:M¿¿2n(TM)¿n:M¿¿2n(TM) intersects the zero section transversally on a codimension one submanifold Z¿MZ¿M. This paper will be a systematic investigation of such Poisson manifolds. In particular, we will study in detail the structure of (M,¿)(M,¿) in the neighborhood 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.

  • Toric actions on b-symplectic manifolds

     Miranda Galceran, Eva; Guillemin, Victor; Pires, Ana Rita; Scott, Geoffrey
    International mathematics research notices
    Vol. Advance Access, num. publiched July 8, p. 1-31
    DOI: 10.1093/imrn/rnu108
    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

    We study Hamiltonian actions on b-symplectic manifolds with a focus on the effective case of half the dimension of the manifold. In particular, we prove a Delzant-type theorem that classifies these manifolds using polytopes that reside in a certain enlarged and decorated version of the dual of the Lie algebra of the torus.

  • Integrable systems and group actions

     Miranda Galceran, Eva
    Central european journal of mathematics
    Vol. 12, num. 2, p. 240-270
    DOI: 10.2478/s11533-013-0333-6
    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.

  • Access to the full text
    Introduction to Poisson Geometry  Open access

     Miranda Galceran, Eva
    International Conference and School on Poisson Geometry in Mathematics and Physics
    p. 1-83
    Presentation's date: 2014
    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

  • Toric b-Poisson manifolds and their generalizations

     Miranda Galceran, Eva
    Belgian Bracket and Quantisation Workshop
    p. 1
    Presentation's date: 2014
    Presentation of work at congresses

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

    The aim of this talk is to show some examples of simple Poisson manifolds which have some common features with symplectic manifolds (including thestudy of group actions). I will start presenting a Delzant theorem for toric b-symplectic manifolds (joint work with Victor Guillemin, Ana Rita Pires and Geoffrey Scott) taking the 2-dimensional case as starting point. Time permitting, I will mention an application to geometric quantization of b-symplectic manifolds. I also plan to report on an ongoing project with Geoffrey Scott on generalizing the notion of b-symplectic manifold. This notion includes other Poisson manifolds which share good properties with b-symplectic manifoldsand seem to have less topological constraints.

  • Access to the full text
    Symplectic and poisson structures with symmetries in interaction  Open access

     Miranda Galceran, Eva
    Barcelona Mathematical Days
    p. 26-
    Presentation's date: 2014
    Presentation of work at congresses

    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

    Hamiltonian actions constitute a central object of study in symplectic geometry. Special attention has been devoted to the toric case. Toric symplectic manifolds provide natural examples of integrable systems and every integrable system on a symplectic manifold is a toric manifold in a neighbourhood of a compact fiber (Arnold–Liouville). The classification of toric symplectic manifolds is given by Delzant’s theorem in terms of the image of the moment map (Delzant polytope)....

  • Access to the full text
    A Poincaré lemma in geometric quantisation  Open access

     Miranda Galceran, Eva; Solha, Romero
    Journal of Geometric Mechanics
    Vol. 5, num. 4, p. 473-491
    DOI: 10.3934/jgm.2013.5.473
    Date of publication: 2013-12
    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 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

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

  • Access to the full text
    Symplectic topology of b-symplectic manifolds  Open access

     Miranda Galceran, Eva; Martinez Torres, David; Frejlich, Pedro
    DOI: arXiv:1312.7329
    Date: 2013-12
    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

    A Poisson manifold (M2n;) isb-symplectic if aVaduaran is transverse to the zero section. In this paper we apply techniques of Symplectic Topology to address global questions pertaining to b-symplectic manifolds. The main results provide constructions of: symplectic submanifolds a la Donaldson, b-symplectic structures on open manifolds by Gromov's h-principle, and of b-symplectic manifolds with a prescribed singular locus, by means of surgeries.

    A Poisson manifold (M2n; ) is b-symplectic if Vn is transverse to the zero section. In this paper we apply techniques of Symplectic Topology to address global questions pertaining to b-symplectic manifolds. The main results provide constructions of: b-symplectic submanifolds a la Donaldson, b-symplectic structures on open manifolds by Gromov's h-principle, and of b-symplectic manifolds with a prescribed singular locus, by means of surgeries.

  • Symmetries of b-manifolds and their generalizations

     Miranda Galceran, Eva
    Focused research workshop on exterior differential systems and lie the theory
    p. 1
    Presentation's date: 2013-12
    Presentation of work at congresses

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

    The aim of this talk is to show some examples of simple Poisson manifolds which have some common features with symplectic manifolds (including the study of group actions). I will start presenting a Delzant theorem for toric b-symplectic manifolds (joint work with Victor Guillemin, Ana Rita Pires and Geoffrey Scott). Time permitting, I will report on an ongoing project with Geoffrey Scott on generalizing the notion of b-symplectic manifold. This notion includes other Poisson manifolds which share good properties with b-symplectic manifolds and seem to have less topological constraints.

  • On geometric quantisation of integrable systems with singularities  Open access

     Barbieri Solha, Romero
    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

    En aquesta tesi es presenta un nou enfoc sobre l'estudi de la quantització geomètrica de sistemes integrables. En aquesta tesi s'estenen uns resultats de Guillemin, Kostant, Rawnsley, Sniatycki i Sternberg sobre quantització geomètrica, considerant les fibracions regulars com polaritzacions reals, pel cas singular. Les polaritzacions reals estudiades en aquesta tesi vénen donades per sistemes integrables amb singularitats no degenerades i la definició de quantització geomètrica utilitzada és la donada per Kostant (via grups de cohomologia superiors). També presentem proves amb un punt de vista unificador de resultats de quantització geomètrica amb òrbites periòdiques utilitzant l'existència d'accions simplèctiques per cercles: les tècniques utilitzades en aquesta tesi subratllen i desembrollen el rol de les accions per cercles en resultats coneguts en quantització geomètrica. Aquesta tesi és original en els següents aspectes. Primer, s'utilitzen les accions de cercles per obtenir resultats en quantizació geomètrica i també s'estudien les obstruccions existència de lemes de Poincaré per cohomologia foliada quan la foliació té singularitats. Els resultats anteriors obtinguts per Rawnsley sobre accions de cercles no s'han pogut utilizar en el cas en què l'acció no sigui lliure, i no és trivial adaptar-los per tenir en compte els punts fixos. Un cop desenvolupades aquestes tècniques, es calcula el la quantització geomètrica en una sèrie de situacions que inclouen el fibrat cotangent d'un cercle i productes d'aquest amb qualsevol varietat simplèctica exacta quantitzada i entorns de singularitats no degenerades d'un sistema integrable (les singularitats hiperbòliques requereixen un estudi diferent perquè no tenen associada cap acció natural per cercles). Aquests càlculs proven que el complex de Kostant dona una resolución fina del feix de seccions planes al llarg de la polarització quan la polarització ve donada per un sistema integrable amb singularitats no degenerades. És important destacar que les demonstracions són originals ja que contràriament al que un podria esperar, no hi ha lema de Poincaré per la cohomologia foliada quan la polarització considerada té singularitats. Aquest resultat no trivial és interessant per se però, en aquesta tesi, només s'inclouen els resultats relacionats amb quantització geomètrica. Per exemple, la necessitat de fer una nova demostració per demostrar que el complex de Kostant dona una resolución fina del feix de seccions planes al llarg de la polarització. Aquesta tesi també conté una nova demostració d'un resultat que primer va ser demostrar per Guillemin i Sternberg sobre el caràcter discret de les òrbites de Bohr-Somerfeld. En aquesta demostració no només es destaca el rol jugat per les accions per cercles pero també es suprimeix una condició de compacitat de l'enunciat del teorema. L'explotació de l'existència d'accions per cercles culmina amb una demostració alternativa dels teoremes de Sniatycki i Hamilton. Es una demostració original i que pretén unificar les anteriors: l'argument funciona en les dues situacions: fibrats Lagrangians i varietats localment tòriques. A més a més, aquest punt de vista aporta llum a una conjectura sobre les contribucions de les singularitats de tipus focus-focus. De fet demostrem que, en grau zero, no hi ha cap contribució a la quantització geomètrica provinent de les fibres focus-focus per varietats semitòriques en dimensió 4.

    This thesis shows an approach to geometric quantisation of integrable systems. It extends some results by Guillemin, Kostant, Rawnsley, Sniatycki and Sternberg in geometric quantisation, considering regular fibrations as real polarisations, to the singular setting: the real polarisations concerned here are given by integrable systems with nondegenerate singularities, and the definition of geometric quantisation used is the one suggested by Kostant (via higher cohomology groups). It also presents unifying proofs for results in geometric quantisation by exploring the existence of symplectic circle actions: the tools developed here highlight and unravel the role played by circle actions in known results in geometric quantisation. The originality of this thesis relies on the following aspects. Firstly, the use of symplectic circle actions to obtain results in geometric quantisation, and secondly, the nonexistence of Poincaré lemmata for foliated cohomology when the foliation has singularities. Previous results on circle actions, due to Rawnsley, could not be used when the circle action is not free, and it is not straightforward to adapt them to accommodate fixed points. After developing these techniques, the computation of geometric quantisation is performed in a series of situations, which includes: the cotangent bundle of the circle and products of it with any quantisable manifold, and neighbourhoods of nondegenerate singularities of integrable systems (hyperbolic singularities need special treatment, since there is no natural circle action). These computations imply that the Kostant complex is a fine resolution (for the sheaf of sections of the prequantum line bundle which are flat along the polarisation) when the real polarisations are given by integrable systems with nondegenerate singularities. It is important to mention that the proofs are original, since, contrary to expectations, there is no Poincaré Lemma when singularities are allowed for the foliated cohomology associated to foliations induced by integrable systems. This nontrivial result turns out to be interesting in its own right, but only the aspects related to geometric quantisation are presented in the thesis, e.g. the need for a new proof that the Kostant complex is a fine resolution for the sheaf of flat sections. The thesis also provides a different proof of a theorem, firstly proved by Guillemin and Sternberg, that shows that the set of regular Bohr-Sommerfeld fibres is discrete -it not only bares the role played by circle actions, it also excludes the compactness assumption from the theorem. The exploitation of circle actions culminate in an alternative proof for the theorems of Sniatycki and Hamilton. It is an original and unifying proof: the argument works for both situations, Lagrangian fibre bundles and locally toric manifolds. In addition, this approach casts some light on a conjecture about the contributions coming from focus-focus type of singularities. It actually proves that, in degree zero, there is no contribution to geometric quantisation coming from focus-focus fibres for compact 4-dimensional almost toric manifolds.

  • Geometry and Dynamics of Integrable Systems

     Miranda Galceran, Eva
    Collaboration in exhibitions

     Share

  • Acta mathematica

     Miranda Galceran, Eva
    Collaboration in journals

     Share

  • Journal of the London Mathematical Society. Second series

     Miranda Galceran, Eva
    Collaboration in journals

     Share

  • Quarterly journal of mathematics

     Miranda Galceran, Eva
    Collaboration in journals

     Share

  • Revisiting normal forms of Poisson structures : from Weinstein to Crainic-Marcut via Conn, Hamilton and Monnier-Zung

     Miranda Galceran, Eva
    Quarterly seminar on Topology and Geometry
    p. 1
    Presentation's date: 2013-02-12
    Presentation of work at congresses

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

  • Internacional : la columna de l'EMS

     Miranda Galceran, Eva
    Date: 2013-02
    Report

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

  • Differential geometry and its applications

     Miranda Galceran, Eva
    Collaboration in journals

     Share

  • Geometry and Dynamics of Integrable Systems

     Miranda Galceran, Eva; Presas, Francisco
    Competitive project

     Share

  • Coupling symmetries with Poisson structures

     Miranda Galceran, Eva; Laurent Gengoux, Camille
    Acta Mathematica Vietnamica
    Vol. 38, num. 1, p. 21-32
    DOI: 10.1007/s40306-013-0008-1
    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
    Vol. 165, num. 1, p. 1-3
    DOI: 10.1007/s10711-013-9868-8
    Date of publication: 2013
    Journal article

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

  • A Poincare lemma in geometric quantisation

     Miranda Galceran, Eva; Solha, Romero
    Date: 2013
    Report

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

    This paper presents a Poincar ´e lemma for the Kostant comple x, used to compute geometric quantisation, when the polarisat ion is given by a Lagrangian foliation defined by an integrable system wit h non- degenerate singularities

  • Access to the full text
    Random test examples with known minimum for convex semi-infinite programming problems  Open access

     Ferrer Biosca, Alberto; Miranda Galceran, Eva
    Date: 2013
    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

    A signi cant research activity has occurred in the area of convex semi- in nite optimization in the recent years. Many new theoretical, algorithm and computational contribution has been obtained . Despite these numerous con- tributions, there still exits a lack of representative convex semi-in nite test problems. Test problems are of major importance for researchers interested in the algorithmic development. This article is motivated by the scarcity of con- vex semi-in nite test problems and describes a procedure for generating convex semi-in nite families of test problems with optimal solution and optimal value known.

  • Access to the full text
    Geometric Quantization of real polarizations via sheaves  Open access

     Miranda Galceran, Eva; Presas, Francisco
    Date: 2013-01
    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

    In this article we develop tools to compute the Geometric Quantization of a symplectic manifold with respect to a regular Lagrangian foliation via sheaf cohomology. The starting point is the definition of representation spaces due to Kostant. We check that the associated sheaf cohomology apparatus satisfies Mayer-Vietoris and K\"unneth formulae. As a consequence, new proofs of classical results for fibrations are obtained. In the general case of Lagrangian foliations, we compute Geometric Quantization with respect to almost any generic regular Lagrangian foliation on a 2-torus.

  • Preface to the special issue of GEDYTO: Geometrical Methods in Dynamics and Topology Hanoi 2011

     Miranda Galceran, Eva; Tien Zung, Nguyen; Ginzburg, Viktor; Duc Thai, Do
    DOI: 10.1007/s40306-013-0013-4
    Date: 2013-01
    Report

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

  • Access to the full text
    On a Poincaré lemma for singular foliations and geometric quantization  Open access

     Miranda Galceran, Eva; Solha, Romero
    Date: 2013-01
    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

    In this paper we prove a Poincar e lemma for forms tangent to a foliation with nondegenerate singularities given by an integrable system on a symplectic manifold. As a consequence, the Kostant complex in Geometric Quantization is a ne resolution of the sheaf of at sections when the polarization is spanned by the Hamiltonian vector elds of the rst integrals of this integrable system.

  • Access to the full text
    Toric actions on b-symplectic manifolds  Open access

     Miranda Galceran, Eva; Pires, Ana Rita; Guillemin, Victor; Scott, Geoffrey
    Date: 2013
    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

    We study Hamiltonian actions on b-symplectic manifolds with a focus on the eective case of half the dimension of the manifold. In particular, we prove a Delzant-type theorem that classies these man- ifolds using polytopes that reside in a certain enlarged and decorated version of the dual of the Lie algebra of the torus. At the end of the paper we suggest further avenues of study, including an example of a toric action on a b2-manifold and applications of our ideas to integrable systems on b-manifolds.

    We study Hamiltonian actions on b-symplectic manifolds with a focus on the e ective case of half the dimension of the manifold. In particular, we prove a Delzant-type theorem that classi es these manifolds using polytopes that reside in a certain enlarged and decorated version of the dual of the Lie algebra of the torus. At the end of the paper we suggest further avenues of study, including an example of a toric action on a b 2-manifold and applications of our ideas to integrable systems on b-manifolds

  • On a Poincaré Lemma for Foliations

     Miranda Galceran, Eva; Solha, Romero
    DOI: 10.1142/9789814556866_0007
    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=

  • Integrable systems and Hamiltonian actions on Poisson manifolds

     Miranda Galceran, Eva
    Conference on Finite Dimensional Integrable Systems
    p. 1
    Presentation's date: 2013
    Presentation of work at congresses

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

    The aim of this talk is to give a flavour of the interplay between integrable systems and Hamiltonian actions in the Poisson setting. In the first part of the talk I will present some normal form results in the neighbourhood of a Liouville torus (action-angle coordinates for commutative and non-commutative integrable systems). In the second part of this talk I will concentrate on two particular examples of integrable systems on Poisson manifolds: The Gelfand-Ceitlin systems and toric b-symplectic manifolds (which are motivated by the study of integrable systems on symplectic manifolds with boundary). Time permitting, some recent results on rigidity of Hamiltonian actions on Poisson manifolds will also be presented.

  • Geometrías simplécticas singulares

     Miranda Galceran, Eva
    Congreso de Jóvenes Investigadores
    p. 1
    Presentation's date: 2013
    Presentation of work at congresses

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

    Esta charla pretende ser una introduccion a los problemas geometricos en variedades de Poisson. Las variedades de Poisson constituyen una general- izacion de las variedades simplecticas cuyo estudio se inicio motivada por nu- merosos sistemas mecanicos. Nos planteamos problemas de formas normales, estudio de simetras y clasicacion global para variedades de Poisson generales que son cuestiones clasicas en el ambito simplectico. Como punto de partida tomaremos el caso de b-variedades simplecticas (con estructura simplectica en un conjunto denso y singulares en una hipersuperfcie ([1], [2])) cuyo estudio se inicio por Melrose y Nest-Tsygan al considerar variedades simplecticas con borde. Acabaremos abordando casos mas complicados dentro del ambito de geometra de Poisson ([6],[7],[3],[4]). Nos interesaremos especialmente en el es- tudio de simetras en estas variedades y en cuestiones de rigidez estructural. El tipo de tecnicas requeridas para este estudio es mas complejo que en el caso simplectico y requiere, en ocasiones, desarrollar tecnicas propias del analisis geometrico como un metodo de Nash-Moser generalizado [7].

  • Normal forms of Poisson structures revisited

     Miranda Galceran, Eva
    Conference in honor of Alan Weistein
    p. 1
    Presentation's date: 2013
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • Geometric quantization of real polarizations

     Miranda Galceran, Eva
    Workshop on Quantization and Reduction
    p. 4
    Presentation's date: 2013
    Presentation of work at congresses

     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
    Vol. 86, p. 31-37
    DOI: DOI: 10.4171/NEWS
    Date of publication: 2012-12-01
    Journal article

     Share Reference managers Reference managers Open in new window

  • 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

  • Hamiltonian actions on Poisson manifolds and an abstract Nash-Moser normal form theorem

     Miranda Galceran, Eva
    Iberoamerican Meeting on Geometry Mechanics and Control
    p. 1
    Presentation's date: 2012-09-06
    Presentation of work at congresses

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

  • 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

  • GESTA 2011: New trends in Symplectic and contact geometry. Geometricae dedicata

     Miranda Galceran, Eva
    Vol. 165, num. 1
    Collaboration in journals

     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
    p. 1-40
    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

  • Action-angle coordinates and geometric quantization

     Miranda Galceran, Eva
    European Congress of Mathematics
    p. 1
    Presentation's date: 2012
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • A Poisson zoo of integrable systems

     Miranda Galceran, Eva
    International Workshop on Integrability in Dynamical Systems and Control
    p. 1
    Presentation's date: 2012
    Presentation of work at congresses

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

  • Rigidity of Hamiltonian actions and a normal form theorem for SCI-spaces

     Miranda Galceran, Eva
    Quarterly seminar on Topology and Geometry
    p. 1
    Presentation's date: 2012
    Presentation of work at congresses

    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
    Vol. 229, num. 2, p. 1136-1179
    DOI: 10.1016/j.aim.2011.09.013
    Date of publication: 2011-11-08
    Journal article

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

  • The Symplectic geometry of b-manifolds

     Miranda Galceran, Eva
    EMS-RSME Joint Mathematical Weekend
    p. 15
    Presentation's date: 2011-10
    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 and back

     Miranda Galceran, Eva
    Joint Mathematical Conference CSASC
    p. 6
    Presentation's date: 2011-09
    Presentation of work at congresses

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