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.
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.
Collections in this community
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Articles de revista [174]
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Reports de recerca [51]
Recent Submissions
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Contact structures with singularities: from local to global
(Elsevier, 2023-10-01)
Article
Open AccessIn 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
(European Mathematical Society (EMS), 2021)
Conference report
Open AccessThe 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
(Springer Nature, 2023-06-13)
Article
Open AccessHomogeneity 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
(Elsevier, 2023-11-15)
Article
Open AccessRobotic 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
(Elsevier, 2023-09-01)
Article
Open AccessThe 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
(Springer Nature, 2022-11-11)
Article
Open AccessIn 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
(Institute of Physics (IOP), 2023-06-06)
Article
Open AccessManifolds 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
(Institute of Physics (IOP), 2023-04-12)
Article
Restricted access - publisher's policyA 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
(2021-02-01)
Article
Open AccessLet 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
(Springer Nature, 2021-07-21)
Conference lecture
Open AccessIn 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
(Springer, 2022-02-21)
Article
Open AccessA 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
(2023-02-01)
Article
Open AccessThis 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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