Enviaments recents

  • Open problems, questions, and challenges in finite-dimensional integrable systems 

    Miranda Galcerán, Eva; Bolsinov, Alexey; Matveev, Vladimir; Tabachnikov, Sergei (2018-04-11)
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    Accés obert
    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)
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    Accés obert
    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)
    Report de recerca
    Accés obert
    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)
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    Accés obert
    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)
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    Accés obert
    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)
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    Accés obert
    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)
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    Accés obert
    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)
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    Accés obert
    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)
    Report de recerca
    Accés obert
    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 ...
  • Homotopy linear algebra 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2016-02)
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    Accés obert
    By homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices ...
  • Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2015-12)
    Report de recerca
    Accés obert
    Decomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors between decomposition spaces induce coalgebra ...
  • Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2015-12)
    Report de recerca
    Accés obert
    This is part 2 of a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in 8-groupoids. A decomposition space ...

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