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 [193]
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Reports de recerca [54]
Recent Submissions
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Quantised Painlevé monodromy manifolds, Sklyanin and Calabi-Yau algebras
(2021-01-06)
Article
Open AccessIn this paper we study quantum del Pezzo surfaces belonging to a certain class. In particular we introduce the generalised Sklyanin-Painlevé algebra and characterise its PBW/PHS/Koszul properties. This algebra contains as ... -
Isomonodromic deformations: confluence, reduction and quantisation
(2023-03-01)
Article
Open AccessIn this paper we study the isomonodromic deformations of systems of differential equations with poles of any order on the Riemann sphere as Hamiltonian flows on the product of co-adjoint orbits of the truncated current ... -
Topological entropy of Turing complete dynamics
(2024-04-10)
Research report
Open AccessWe explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call “regular Turing machines” (which includes most of ... -
Canonical lifts in multisymplectic De Donder-Weyl Hamiltonian field theories
(2024-08-01)
Article
Open AccessWe define canonical lifts of vector fields to the multisymplectic multimomentum bundles of De Donder–Weyl Hamiltonian (first-order) field theories and to the appropriate premultisymplectic embedded constraint submanifolds ... -
On Darboux theorems for geometric structures induced by closed forms
(springer-Verlag, 2024-06-20)
Article
Open AccessThis work reviews the classical Darboux theorem for symplectic, presymplectic, and cosymplectic manifolds (which are used to describe mechanical systems), as well as certain cases of multisymplectic manifolds, while extends ... -
A novel algebraic approach to time-reversible evolutionary models
(Society for Industrial and Applied Mathematics (SIAM), 2024-01-01)
Article
Open AccessIn recent years, algebraic tools have been proven useful in phylogenetic reconstruction and model selection through the study of phylogenetic invariants. However, up to now, the models studied from an algebraic viewpoint ... -
Darboux, Moser and Weinstein theorems for prequantum systems and applications to geometric quantization
(2024-12)
Article
Open AccessWe establish analogs of the Darboux, Moser and Weinstein theorems for prequantum systems. We show that two prequantum systems on a manifold with vanishing first cohomology, with symplectic forms defining the same cohomology ... -
Darboux, Moser and Weinstein theorems for prequantum systems
(2024-05-23)
Research report
Open AccessWe establish analogs of the Darboux, Moser and Weinstein theorems for prequantum systems. We show that two prequantum systems on a manifold with vanishing first cohomology, with symplectic forms defining the same cohomology ... -
Towards a fluid computer
(2024-04-01)
Research report
Open AccessIn 1991, Moore [20] raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao [25] asked whether a mechanical system, including a fluid flow, can simulate a universal ... -
Asymptotic analysis of near-field coupling in massive MISO and massive SIMO systems
(2024-08)
Article
Open AccessThis paper studies the receiver to transmitter antenna coupling in near-field communications with massive arrays. Although most works in the literature consider that it is negligible and approximate it by zero, there is ... -
The Arnold conjecture for singular symplectic manifolds
(Springer, 2024-04-18)
Article
Open AccessIn this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of bm-symplectic manifolds. Novel techniques are introduced to associate smooth symplectic ... -
A novel collision model for inextensible textiles and its experimental validation
(Elsevier, 2024-04)
Article
Open AccessIn this work, we introduce a collision model specifically tailored for the simulation of inextensible textiles. The model considers friction, contacts, and inextensibility constraints all at the same time without any ...
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