Enviaments recents

  • 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)
    Report de recerca
    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)
    Report de recerca
    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)
    Report de recerca
    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)
    Report de recerca
    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)
    Report de recerca
    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)
    Report de recerca
    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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