GEOMVAP - Geometria de Varietats i Aplicacions

 

L'objectiu general del grup és aprofundir en l'estudi d'estructures geomètriques i les seves aplicacions. Les estructures geomètriques considerades són varietats algebraiques, simplèctiques o diferenciables i les seves aplicacions es centren principalment als camps de la biologia, la robòtica, la física, els sistemes dinàmics i la mecànica celeste. Per fer-ho utilitzarem diverses eines (geomètriques, algebraiques, topològiques, aritmètiques, diferencials i computacionals) i en moltes ocasions fusionarem tècniques provinent de diversos àmbits. Membres del grup treballen dintre d'equips pluridisciplinars i en línies de recerca transversals.

http://futur.upc.edu/GEOMVAP

Recent Submissions

  • An invitation to singular symplectic geometry 

    Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Dempsey Bradell, Roisin Mary; Oms, Cedric; Planas Bahí, Arnau (2017)
    Article
    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 ...

  • Classification of b^m-Nambu structures of top degree 

    Miranda Galcerán, Eva; Planas Bahí, Arnau (2018-01)
    Article
    Open Access
    We obtain sufficient conditions for the existence and uniqueness of a positive compact almost automorphic solution to a logistic equation with discrete and continuous delay. Moreover, we provide a counterexample to some ...

  • Constancy regions of mixed multiplier ideals in two-dimensional local rings with rational singularities 

    Alberich Carramiñana, Maria; Alvarez Montaner, Josep; Dachs Cadefau, Ferran (WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2018)
    Article
    Open Access
    The aim of this paper is to study mixed multiplier ideals associated with a tuple of ideals in a two-dimensional local ring with a rational singularity. We are interested in the partition of the real positive orthant given ...

  • 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 ...

  • New algebraic conditions for the identification of the relative position of two coplanar ellipses 

    Alberich Carramiñana, Maria; Elizalde, Borja; Thomas, Federico (2017-05-01)
    Article
    Restricted access - publisher's policy
    The identification of the relative position of two real coplanar ellipses can be reduced to the identification of the nature of the singular conics in the pencil they define and, in general, their location with respect to ...

  • 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. ...

  • Effective computation of base points of ideals in two-dimensional local rings 

    Alberich Carramiñana, Maria; Álvarez Montaner, Josep; Blanco Fernández, Guillem (2018-01-04)
    Article
    Restricted access - publisher's policy
    © 2018 Elsevier Ltd. We provide an algorithm that allows to describe the minimal log-resolution of an ideal in a smooth complex surface from the minimal log-resolution of its generators. In order to make this algorithm ...

  • Homotopy linear algebra 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2018-04)
    Article
    Open Access
    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 ...

  • The inertia of the symmetric approximation for low-rank matrices 

    Casanellas Rius, Marta; Fernández Sánchez, Jesús; Garrote López, Marina (Taylor & Francis, 2017-11-10)
    Article
    Restricted access - publisher's policy
    © 2017 Informa UK Limited, trading as Taylor & Francis Group In many areas of applied linear algebra, it is necessary to work with matrix approximations. A usual situation occurs when a matrix obtained from experimental ...

  • D-modules, Bernstein-Sato polynomials and F-invariants of direct summands 

    Álvarez Montaner, Josep; Huneke, Craig; Núñez-Betancourt, Luis (2017-12-01)
    Article
    Restricted access - publisher's policy
    We study the structure of D -modules over a ring R which is a direct sum- mand of a polynomial or a power series ring S with coefficients over a field. We relate properties of D -modules over R to D -modules over S . We ...

  • The matter-ekpyrotic bounce scenario in Loop Quantum Cosmology 

    Haro Cases, Jaume; Amorós Torrent, Jaume; Aresté Saló, Llibert (2017-09-01)
    Article
    Restricted access - publisher's policy
    We will perform a detailed study of the matter-ekpyrotic bouncing scenario in Loop Quantum Cosmology using the methods of the dynamical systems theory. We will show that when the background is driven by a single scalar ...

  • Godement resolution and operad sheaf homotopy theory 

    Rodríguez González, Beatriz; Roig Martí, Agustín (2017-08-08)
    Article
    Restricted access - publisher's policy
    We show how to induce products in sheaf cohomology for a wide variety of coefficients: sheaves of dg commutative and Lie algebras, symmetric Omega-spectra, filtered dg algebras, operads and operad algebras.

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