Recent Submissions

  • A Poincaré lemma in geometric quantisation 

    Miranda Galcerán, Eva; Solha, Romero (2013)
    External research report
    Open Access
    This paper presents a Poincaré 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.
  • Convexity for Hamiltonian torus actions on b-symplectic manifolds 

    Guillemin, Victor; Miranda Galcerán, Eva; Pires, Ana Rita; Scott, Geoffrey (2014-12)
    External research report
    Open Access
    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 ...
  • Desingularizing b^m-symplectic structures 

    Miranda Galcerán, Eva (2015-12)
    External research report
    Open Access
    A 2n-dimensional Poisson manifold (M,¿) is said to be bm-symplectic if it is symplectic on the complement of a hypersurface Z and has a simple Darboux canonical form at points of Z which we will describe below. In this ...
  • Cotangent models for integrable systems on $b$-symplectic manifolds 

    Miranda Galcerán, Eva; Kiesenhofer, Anna (2016-01)
    External research report
    Open Access
  • Equivariant classification of bm-symplectic surfaces and Nambu structures 

    Miranda Galcerán, Eva; Planas, Arnau (2016)
    External research report
    Open Access
    In this paper we extend the classification scheme in [S] for bm-symplectic surfaces, and more generally, bm-Nambu structures to the equivariant setting. When the compact group is the group of deck-transformations of an ...
  • From action-angle coordinates to geometric quantization 

    Miranda Galcerán, Eva (2011-03-01)
    External research report
    Open Access
    The philosophy of geometric quantization is to ¯nd and understand a \(one-way) dictionary" that \translates" classical systems into quantum systems . In this way, a quantum system is associated to a classical system in ...
  • Up-to-homotopy algebras with strict units 

    Roig Martí, Agustín (2018-12-20)
    External research report
    Open Access
    We prove the existence of minimal models à la Sullivan for operads with non trivial arity zero. So up-to-homotopy algebras with strict units are just operad algebras over these minimal models. As an application we give ...
  • Contact structures with singularities 

    Miranda Galcerán, Eva; Oms, Cédric (2018-06-15)
    External research report
    Open Access
    We study singular contact structures, which are tangent to a given smooth hypersurface Z and satisfy certain transversality conditions. These singular contact structures are determined by the kernel of non-smooth differential ...
  • Open problems, questions, and challenges in finite-dimensional integrable systems 

    Miranda Galcerán, Eva; Bolsinov, Alexey; Matveev, Vladimir; Tabachnikov, Sergei (2018-04-11)
    External research report
    Open Access
    The paper surveys open problems and questions related to different aspects of integrable systems with finitely many degrees of freedom. Many of the open problems were suggested by the participants of the conference ...
  • The geometry of E-manifolds 

    Miranda Galcerán, Eva (2018-02-09)
    External research report
    Open Access
    Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an E-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. ...
  • Geometric quantization of semitoric systems and almost toric manifolds 

    Miranda Galcerán, Eva; Presas, Francisco; Solha, Romero (2017)
    External research report
    Open Access
    Kostant gave a model for the real geometric quantization associated to polarizations via the cohomology associated to the sheaf of flat sections of a pre-quantum line bundle. This model is well-adapted for real polarizations ...
  • An invitation to singular symplectic geometry 

    Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Planas Bahí, Arnau; Oms, Cedric; Dempsey Bradell, Roisin Mary (2017)
    External research report
    Open Access
    In this paper we analyze in detail a collection of motivating examples to consider bm- symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every bm-symplectic ...

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