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

  • Contact structures with singularities: from local to global 

    Miranda Galcerán, Eva; Oms, Cédric (Elsevier, 2023-10-01)
    Article
    Open Access
    In this article we introduce and analyze in detail singular contact structures, with an emphasis on bm -contact structures, which are tangent to a given smooth hypersurface Z and satisfy certain transversality conditions. ...
  • Looking at Euler flows through a contact mirror: universality and undecidability 

    Cardona Aguilar, Robert; Miranda Galcerán, Eva; Peralta-Salas, Daniel (European Mathematical Society (EMS), 2021)
    Conference 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 by Cardona, Miranda, and Peralta- Salas, several unknown facets of the Euler flows ...
  • Designing weights for quartet-based methods when data are heterogeneous across lineages 

    Casanellas Rius, Marta; Fernández Sánchez, Jesús; Garrote López, Marina; Sabaté Vidales, Marc (Springer Nature, 2023-06-13)
    Article
    Open Access
    Homogeneity across lineages is a general assumption in phylogenetics according to which nucleotide substitution rates are common to all lineages. Many phylogenetic methods relax this hypothesis but keep a simple enough ...
  • A representation of cloth states based on a derivative of the Gauss linking integral 

    Coltraro Ianniello, Franco; Fontana, Josep; Amorós Torrent, Jaume; Alberich Carramiñana, Maria; Borràs Sol, Júlia; Torras, Carme (Elsevier, 2023-11-15)
    Article
    Open Access
    Robotic manipulation of cloth is a complex task because of the infinite-dimensional shape-state space of textiles, which makes their state estimation very difficult. In this paper we introduce the dGLI Cloth Coordinates, ...
  • Universality of Euler flows and flexibility of Reeb embeddings 

    Cardona Aguilar, Robert; Miranda Galcerán, Eva; Peralta Salas, Daniel; Presas, Francisco (Elsevier, 2023-09-01)
    Article
    Open Access
    The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao [38], [39] launched a programme to address the global existence problem for the Euler and ...
  • Optimal control, contact dynamics and Herglotz variational problem 

    de León Rodríguez, Manuel; Lainz Valcázar, Manuel; Muñoz Lecanda, Miguel Carlos (Springer Nature, 2022-11-11)
    Article
    Open Access
    In this paper, we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin maximum principle. As an important result, among others, we develop a contact Pontryagin maximum ...
  • Hamiltonian facets of classical gauge theories on E-manifolds 

    Mir Garcia, Pau; Miranda Galcerán, Eva; Nicolás Martínez, Pablo (Institute of Physics (IOP), 2023-06-06)
    Article
    Open Access
    Manifolds with boundary, with corners, b-manifolds and foliations model configuration spaces for particles moving under constraints and can be described as E-manifolds. E-manifolds were introduced in Nest and Tsygan (2001 ...
  • Sundman transformation and alternative tangent structures 

    Cariñena Marzo, José Fernando; Martínez Fernandez, Eduardo; Muñoz Lecanda, Miguel Carlos (Institute of Physics (IOP), 2023-04-12)
    Article
    Restricted access - publisher's policy
    A geometric approach to Sundman transformation defined by basic functions for systems of second-order differential equations is developed and the necessity of a change of the tangent structure by means of the function ...
  • Noetherian rings of low global dimension and syzygetic prime ideals 

    Planas Vilanova, Francesc d'Assís (2021-02-01)
    Article
    Open Access
    Let R be a Noetherian ring. We prove that R has global dimension at most two if, and only if, every prime ideal of R is of linear type. Similarly, we show that R has global dimension at most three if, and only if, every ...
  • The Herglotz principle and vakonomic dynamics 

    Muñoz Lecanda, Miguel Carlos; De León, Manuel; Lainz Valcázar, Manuel (Springer Nature, 2021-07-21)
    Conference lecture
    Open Access
    In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we ...
  • Infinitesimal time reparametrisation and its applications 

    Cariñena Marzo, José Fernando; Martínez Fernandez, Eduardo; Muñoz Lecanda, Miguel Carlos (Springer, 2022-02-21)
    Article
    Open Access
    A geometric approach to Sundman infnitesimal time-reparametrisation is given and some of its applications are used to illustrate the general theory. Special emphasis is put on geodesic motions and systems described by ...
  • More insights into symmetries in multisymplectic field theories 

    Guerra IV, Arnoldo; Román Roy, Narciso (2023-02-01)
    Article
    Open Access
    This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in ...

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