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.

El objetivo general del grupo es profundizar en el estudio de estructuras geométricas y sus aplicaciones. Las estructuras geométricas consideradas son variedades algebraicas, simplécticas o diferenciables y sus aplicaciones se centran principalmente en los campos de la biología, la robótica, la física, los sistemas dinámicos y la mecánica celeste. Para ello utilizamos varias herramientas (geométricas, algebraicas, topológicas, aritméticas, diferenciales y computacionales) y en muchas ocasiones fusionamos técnicas procedentes de diversos ámbitos. Algunos miembros del grupo trabajan dentro de equipos pluridisciplinares y en líneas de investigación transversales.

El objetivo general del grupo es profundizar en el estudio de estructuras geométricas y sus aplicaciones. Las estructuras geométricas consideradas son variedades algebraicas, simplécticas o diferenciables y sus aplicaciones se centran principalmente en los campos de la biología, la robótica, la física, los sistemas dinámicos y la mecánica celeste. Para ello utilizamos varias herramientas (geométricas, algebraicas, topológicas, aritméticas, diferenciales y computacionales) y en muchas ocasiones fusionamos técnicas procedentes de diversos ámbitos. Algunos miembros del grupo trabajan dentro de equipos pluridisciplinares y en líneas de investigación transversales.

El objetivo general del grupo es profundizar en el estudio de estructuras geométricas y sus aplicaciones. Las estructuras geométricas consideradas son variedades algebraicas, simplécticas o diferenciables y sus aplicaciones se centran principalmente en los campos de la biología, la robótica, la física, los sistemas dinámicos y la mecánica celeste. Para ello utilizamos varias herramientas (geométricas, algebraicas, topológicas, aritméticas, diferenciales y computacionales) y en muchas ocasiones fusionamos técnicas procedentes de diversos ámbitos. Algunos miembros del grupo trabajan dentro de equipos pluridisciplinares y en líneas de investigación transversales.

Recent Submissions

  • Bernstein-Sato polynomials in commutative algebra 

    Álvarez Montaner, Josep; Jeffries, Jack; Núñez-Betancourt, Luis (Springer Nature, 2022-02-23)
    Part of book or chapter of book
    Restricted access - publisher's policy
    This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra
  • An inextensible model for the robotic manipulation of textiles 

    Coltraro Ianniello, Franco; Amorós Torrent, Jaume; Alberich Carramiñana, Maria; Torras, Carme (2022-01-01)
    Article
    Open Access
    We introduce a new isometric strain model for the study of the dynamics of cloth garments in a moderate stress environment, such as robotic manipulation in the neighborhood of humans. This model treats textiles as surfaces ...
  • An open set of 4×4 embeddable matrices whose principal logarithm is not a Markov generator 

    Casanellas Rius, Marta; Fernández Sánchez, Jesús; Roca Lacostena, Jordi (Taylor & Francis, 2020-12-17)
    Article
    Open Access
    A Markov matrix is embeddable if it can represent a homogeneous continuous-time Markov process. It is well known that if a Markov matrix has real and pairwise-different eigenvalues, then the embeddability can be determined ...
  • The groupoid of finite sets is biinitial in the 2-category of rig categories 

    Elgueta Montó, Josep (2021-11-01)
    Article
    Restricted access - publisher's policy
    The groupoid of finite sets has a “canonical” structure of a symmetric 2-rig with the sum and product respectively given by the coproduct and product of sets. This 2-rig ^ FSet is just one of the many non-equivalent ...
  • A K-contact Lagrangian formulation for nonconservative field theories 

    Gaset Rifà, Jordi; Gràcia Sabaté, Francesc Xavier; Muñoz Lecanda, Miguel Carlos; Rivas Guijarro, Xavier; Román Roy, Narciso (2021-06-01)
    Article
    Restricted access - publisher's policy
    Dynamical systems with dissipative behaviour can be described in terms of contact manifolds and a modified version of Hamilton's equations. Dissipation terms can also be added to field equations, as showed in a recent paper ...
  • Skinner–Rusk formalism for k-contact systems 

    Gràcia Sabaté, Francesc Xavier; Rivas Guijarro, Xavier; Román Roy, Narciso (2022-02-01)
    Article
    Open Access
    In previous papers, a geometric framework has been developed to describe non-conservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of k-contact Hamiltonian ...
  • On the singular Weinstein conjecture and the existence of escape orbits for b-Beltrami fields 

    Miranda Galcerán, Eva; Oms, Cédric; Peralta-Salas, Daniel (2021-10-07)
    Research report
    Open Access
    Motivated by Poincare’s orbits going to infinity in the (restricted) three-body problem ´ (see [29] and [7]), we investigate the generic existence of heteroclinic-like orbits in a neighbourhood of the critical set of a ...
  • Integrable systems on singular symplectic manifolds: from local to global 

    Miranda Galcerán, Eva; Cardona, Robert (2021-02-03)
    Research report
    Open Access
    In this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes ...
  • Turing universality of the incompressible Euler equations and a conjecture of Moore 

    Miranda Galcerán, Eva; Cardona, Robert; Peralta-Salas, Daniel (2021-04-09)
    Research report
    Open Access
    In this article we construct a compact Riemannian manifold of high dimension on which the time dependent Euler equations are Turing complete. More precisely, the halting of any Turing machine with a given input is equivalent ...
  • Geometric quantization via cotangent models 

    Miranda Galcerán, Eva; Mir Garcia, Pau (2022-05-05)
    Research report
    Open Access
    In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the ...
  • Computability and Beltrami fields in Euclidean space 

    Miranda Galcerán, Eva; Peralta Salas, Daniel; Cardona, Robert (2022-11-15)
    Research report
    Open Access
    In this article, we pursue our investigation of the connections between the theory of computation and hydrodynamics. We prove the existence of stationary solutions of the Euler equations in Euclidean space, of Beltrami ...
  • Looking at Euler flows through a contact mirror: universality and undecidability 

    Miranda Galcerán, Eva; Peralta-Salas, Daniel; Cardona, Robert (2022-07-08)
    Research report
    Open Access
    The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. In recent papers [5, 6, 7, 8] several unknown facets of the Euler flows have been discovered, including ...

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