Recent Submissions

  • 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 ...
  • Decomposition spaces in combinatorics 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2016-12)
    External research report
    Open Access
    A decomposition space (also called unital 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to homotopy) composition, the new ...
  • Three Hopf algebras and their common simplicial and categorical background 

    Gálvez Carrillo, Maria Immaculada; Kaufmann, Ralph L.; Tonks, Andrew (2016-07)
    External research report
    Open Access
    We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebras of Goncharov for multiple zeta values, that of Connes--Kreimer ...
  • Sullivan minimal models of operad algebras 

    Roig Martí, Agustín; Cirici, Joana (2016-12-12)
    External research report
    Open Access
    We prove the existence of Sullivan minimal models of operad algebras, for a quite wide family of operads in the category of complexes of vector spaces over a field of characteristic zero. Our construction is an adaptation ...
  • Non-commutative integrable systems on b-symplectic manifolds 

    Miranda Galcerán, Eva; Kiesenhofer, Anna (2016)
    External research report
    Open Access
    In this paper we study non-commutative integrable systems on b-Poisson manifolds. One important source of examples (and motiva- tion) of such systems comes from considering non-commutative systems on manifolds with ...
  • Examples of integrable and non-integrable systems on singular symplectic manifolds 

    Delshams Valdés, Amadeu; Miranda Galcerán, Eva; Kiesenhofer, Anna (2016-12)
    External research report
    Open Access
    We present a collection of examples borrowed from celes- tial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization trans- formations, Appell's ...

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