{"id":26,"date":"2025-07-20T22:53:03","date_gmt":"2025-07-20T20:53:03","guid":{"rendered":"https:\/\/wp.ull.es\/8ibmgmft\/?page_id=26"},"modified":"2026-02-02T22:53:25","modified_gmt":"2026-02-02T21:53:25","slug":"programme","status":"publish","type":"page","link":"https:\/\/wp.ull.es\/8ibmgmft\/programme\/","title":{"rendered":"PROGRAMME"},"content":{"rendered":"\t\t
\n\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t\t

Plenary Speaker<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t

Paula Balseiro (UFF, Brazil)<\/strong><\/h3>\n

Title:<\/strong> \u00a0On conserved measures for nonholonomic systems with symmetries [slides<\/a>]<\/em>
Abstract:<\/strong> One of the principal differences between Hamiltonian systems\u2014described on symplectic manifolds\u2014and nonholonomic systems is the existence of an invariant volume for the dynamics. However, certain nonholonomic systems also admit an invariant measure. In this talk, we consider nonholonomic systems reduced by the action of a Lie group of symmetries. Under suitable assumptions, we explore the existence of an invariant volume for the underlying geometric structure. This viewpoint provides a geometric insight into the problem; moreover, as a direct consequence, this volume is preserved by the reduced nonholonomic dynamics.
This is joint work with J.C. Marrero and N. Sansonetto.<\/p>\n

Angel Ballesteros (University of Burgos, Spain)<\/strong><\/h3>\n

Title:<\/strong> From quantum reference frames to Poisson-Lie groups\u00a0<\/em><\/p>\n

Abstract:<\/strong> The necessity of considering \u201cquantum reference frames\u201d, namely reference frames associated to dynamical material systems obeying the laws of
quantum theory, has been recently stressed both from quantum information and quantum gravity perspectives. In this talk recent results providing a novel group-
theoretical framework for such quantum reference frames will be presented. In particular, we demonstrate a correspondence between certain quantum
reference frame transformations and transformations generated by a quantum group deformation of the centrally extended Galilei group. In this approach,
since Poisson-Lie groups are just the semiclassical counterpart of quantum groups, the classification of Poisson-Lie structures on the Galilei group
becomes essential in order to identify and construct the appropriate quantum Galilei group. Moreover, the relativistic generalization of this result can be envisaged by considering a suitable Poisson-Lie structure on the Poincar\u00e9 group and by constructing its associated quantum group deformation.<\/p>\n

Mar\u00eda Barbero (Technical University of Madrid, Spain)\u00a0<\/strong><\/h3>\n

Title:\u00a0<\/strong>Discretization maps in optimal control theory {slides<\/a>]<\/em><\/p>\n

Abstract:\u00a0<\/strong>We have recently introduced in the literature a generalization of retraction maps called discretization maps. They are useful to obtain symplectic numerical integrators by adapting the continuous problem to the discretization rule rather than viceversa, as typically done in numerical integration. Consequently, the manifold where the equations of motion live are discretized, in stead of discretizing the equations.<\/p>\n

We will describe how discretization maps can be used to define numerical integrators for optimal control problems so that some structure is preserved.<\/p>\n

Alessandro Bravetti (University of Camerino, Italy)<\/strong><\/h3>\n

Title:<\/strong>\u00a0A Geometric Perspective on Asymmetric Relaxation Dynamics [slides<\/a>]<\/em><\/p>\n

Abstract:<\/strong> Asymmetric relaxation toward equilibrium is a recently-identified phenomenon that has attracted increasing attention in the study of thermodynamic systems. In this talk, we introduce a geometric approach based on gradient flows on appropriate manifolds to describe relaxation dynamics. This framework allows us to formulate a general criterion for determining the emergence of asymmetry in the approach to equilibrium. We conclude by outlining future perspectives and potential extensions.<\/p>\n

Alejandro Cabrera (UFRJ, Brazil)<\/strong><\/h3>\n

Title:<\/strong> Local symplectic groupoids, multiplication, and Poisson integrators [slides<\/a>]<\/em><\/p>\n

Abstract:<\/strong> This talk is based on joint work in progress with D. Iglesias and J.C. Marrero. First, we shall overview the role of local symplectic groupoids in the
construction of Poisson integrators, following O. Cosserat, as well as recent joint work with D. Martin de Diego and M. Vaquero about using approximate
geometric data. We observe that only the &quot;strict bi-realization&quot; data is used in these approaches, but not groupoid multiplication. We then explain how multiplication &quot;m&quot; can be incorporated into this construction and, also, how generating functions for m can be incorporated yielding a practical numerical algorithm. Finally, we show some illustrative examples and discuss future directions.<\/p>\n

Alberto Ibort (University Carlos III\u00a0 of Madrid, Spain)<\/strong>\u00a0 \u00a0<\/h3>\n

Title:<\/span><\/b>\u00a0<\/span>The multisymplectic formalism for field theories revisited<\/span><\/em>
<\/span>Abstract:<\/span><\/b>\u00a0<\/span>The multisymplectic formalism for field theories, so relevant in the description of first order Hamiltonian field theories, will be revisited focusing the attention on its extension to higher order field theories.\u00a0 A novel construction that would provide the dual version of the infinite jet bundle will be presented and discussed.<\/span><\/p>\n

Eduardo Garc\u00eda R\u00edo (University of Santiago de Compostela)<\/strong><\/h3>\n

Title:<\/strong> Ricci solitons on Lie groups [slides<\/a>]<\/span><\/em><\/p>\n

Abstract:<\/strong> Ricci solitons, being self-similar solutions of the Ricci flow have received special attention during the last years. Although a complete description
of such metris is far from being complete, they are quite well-understood in the homogeneous setting. For instance, Riemannian Ricci solitons on Lie groups
are homothetic to algebraic ones.
The Lorentzian situation is much richer, allowing the existence of many Ricci solitons without Riemannian counterpart. Hence our main purpose is to present some classification results for Ricci solitons on low-dimensional Lorentzian Lie groups. We show that any four-dimensional Lie group admits a Ricci soliton left-
invariant Lorentzian metric. As a consequence some non-Einstein compact Lorentzian Ricci solitons are constructed in dimensions three and four.
(This is joint work with Rosal\u00eda Rodr\u00edguez-Gigirey and Ram\u00f3n V\u00e1zquez- Lorenzo)<\/p>\n

Francoise Gay-Balmaz (Nanyang Technological University, Singapur)<\/strong><\/h3>\n

Title:<\/strong> General Relativistic Fluids: Reduction by Symmetries and Junction <\/em>Conditions [slides<\/a>]<\/em><\/p>\n

Abstract:<\/strong> We introduce a new Lagrangian variational framework for general relativistic fluids, allowing symmetry reduction in the relativistic context. By
including Gibbons-Hawking-York (GHY) boundary terms, this approach naturally produces the Israel-Darmois junction conditions, connecting the fluid\u2019s
internal dynamics to the gravitational field in the exterior spacetime.<\/p>\n

Katarzyna\u00a0Grabowska (University of Warsaw, Poland)<\/h3>\n

Title:<\/strong> Affine Dirac aglebroids in nonholonomic mechanics [slides<\/a>]<\/em>
Abstract:<\/strong> The concept of a Dirac algebroid, a linear almost Dirac structure on a vector bundle, was introduced to generate phase equations for mechanical
systems with linear nonholonomic constraints. It was successfully applied to systems described by the so-called mechanical Lagrangian or Hamiltonian, as well as systems with magnetic-like or gyroscopic potentials. In contrast to other structures reported in the literature in this context, the Dirac algebroid we use is built only from constraints and canonical geometric structures of the underlying bundles and is universal, in the sense that it is independent of the particular Hamiltonian or Lagrangian. This approach can be readily generalized to affine nonholonomic constraints via the concept of an affine Dirac algebroid. During the talk, we will recall the main ideas and provide examples.<\/p>\n

References
[1] Grabowska, K., and Grabowski, J. Dirac algebroids in Lagrangian and Hamiltonian mechanics, Journal of Geometry and Physics, 61 (2011),\u00a02233\u20132253.
[2] Garc\u00eda-Naranjo, L. C., Marrero, J. C., de Diego, D. M., and Vald\u00e9s, E. P. P. Almost-Poisson brackets for nonholonomic systems with gyroscopic terms and Hamiltonisation, J Nonlinear Sci 32 (2024)
[3] Grabowska K, Borczy\u0144ska M., Majsak J., and Sobczak, T. Dirac structures in. nonholonomic mechanics, arXiv:2504.18853<\/p>\n

Janusz Grabowski (IMPAN, Poland)<\/h3>\n
\n
Title:<\/strong> Lifting contact and Jacobi structures [slides<\/a>]<\/em><\/div>\n
Abstract:<\/strong> Contact structures, understood as maximally non-integrable hyperplane distributions, admit canonical symplectizations in the form of<\/div>\n
homogeneous symplectic principal bundles with structure group \u211d \u00d7 , the multiplicative group of nonzero real numbers.<\/div>\n
A natural generalization of this picture is given by principal \u211d \u00d7 -bundles endowed with homogeneous Poisson structures \u2014 Poissonizations of Jacobi structures understood as Jacobi bundles, as introduced by Marle [3]. This correspondence was further generalized in our joint work [1] with D. Iglesias, J. C. Marrero, E. Padr\u00f3n, and P. Urb\u00e1nski.We will present an\u00a0 introduction to Jacobi structures defined by Lie brackets on sections of line bundles, together with the construction of their canonical Poissonizations. We will also discuss tangent and phase lifts of principal \u211d- actions, which can be used to lift Jacobi structures and to associate Lie algebroids with Jacobi bundles. This approach goes back to an earlier joint paper [2] with G. Marmo. As a particular example, we will describe a canonical lift of contact structures \u2014 an analogue of the tangent lift of symplectic forms.<\/div>\n
\u00a0<\/div>\n
References<\/strong><\/div>\n
[1] J. Grabowski, D. Iglesias, J. C. Marrero, E. Padr\u00f3n, P. Urb\u00e1nski, Poisson-\u00a0Jacobi reduction of homogeneous tensors, J. Phys. A, 37 (2004), 5383\u20135399.<\/span><\/div>\n
[2] J. Grabowski, G. Marmo, Jacobi structures revisited, J. Phys. A 34 (2001),\u00a010975\u201310990.<\/span><\/div>\n
[3] C. M. Marle, On Jacobi manifolds and Jacobi bundles, in \u201dSymplectic\u00a0geometry, groupoids, and integrable systems\u201d (Berkeley, CA, 1989), 227\u2013246,<\/span><\/div>\n
Math. Sci. Res. Inst. Publ. 20, Springer,New York, 1991.<\/div>\n<\/div>\n

Sergio Grillo (Instituto Balseiro, Bariloche, Argentina)<\/h3>\n

Title:<\/strong> Variational reduction of homogeneous presymplectic Hamiltonian systems [slides<\/a>]<\/em><\/p>\n

Abstract:<\/strong> Given a homogeneous (symplectic) Hamiltonian system on a manifold $M$, with respect to a principal action $\\mathbb{R}^{+}\\times M\\rightarrow M$, we have shown in a previous paper that an associated reduced system can be defined (unless locally), and it is given by a contact Hamiltonian system on $M\/\\mathbb{R}^{+}$. Moreover, we have written a related reconstruction equation and solved it up to quadratures. In this talk we extend our study to the case of homogeneous pre-symplectic Hamiltonian systems, but focusing on the variational formulation of them. We show that (unless locally) a reduced variational principle can be associated to such systems, in such a way that the trajectories of the original system can be reconstructed from the critical points of the mentioned reduced principle. As a by-product, we obtain a variational formulation for all the contact Hamiltonian systems, which offers an alternative to the so-called Herglotz variational principle.<\/p>\n

Manuel de Le\u00f3n (ICMAT-CSIC and Real academia de Ciencias de Espa\u00f1a, Spain)<\/h3>\n
\n

Title: <\/span><\/b>New geometric structures in thermodynamics [slides<\/a>]<\/span><\/em><\/span><\/p>\n

Abstract:<\/strong><\/span>\u00a0<\/span>Traditionally, the geometry of equilibrium thermodynamics has been mainly studied via contact geometry; in this geometric setting, thermodynamic properties are encoded by Legendre submanifolds of the thermodynamic phase space. In this lecture, we will show how different thermodynamic systems can be described using new geometric structures called partially cosymplectic and partially cosymplectic structures of higher order. Indeed, partially cosymplectic structures could be considered as natural extensions of contact geometry, even if they exhibit very different features. This geometric approach allows us to obtain discretisations of the thermodynamic systems and construct very convenient numerical integrators.<\/span><\/p>\n<\/div>\n

Giuseppe Marmo (University of Napoli)<\/h3>\n

Title:<\/strong>\u00a0Differential Geometry of Quantum Evolution [slides<\/a>]<\/em><\/p>\n

Abstract:\u00a0<\/strong>The description of any physical system requires the identification of:\u00a0Observables, say O; States, say S; A probability map pairing observables and states with values in\u00a0probability measures on the real line; Evolution equations of motion; A composition\/decomposition\u00a0rule for composing\/decomposing systems.\u00a0<\/p>\n

In this talk we shall consider as primary choice the evolution on the manifold of\u00a0observables, i.e., we take a dynamical point of view rather than a kinematical one. The additional structures which are required on observables or states because of the physical\u00a0interpretation shall be compatible with a given dynamics. This statement is usually implemented\u00a0 by requiring that the Lie derivative, with respect to the vector field describing the evolution ,of the\u00a0 tensor fields describing the additional geometrical structures identically vanishes. This ideology is fully developed in the book Geometry from Dynamics, Classical and\u00a0 Quantum, there Quantum Mechanics is considered in the Hilbert Space picture and the evolution\u00a0 is given by a vector field on the manifold of states.\u00a0<\/p>\n

Here we consider Quantum Mechanics in the C*-algebraic setting, evolution being described by a\u00a0vector field on the manifold of observables. We will show that alternative structures of Lie-Jordan\u00a0 algebras on the manifold of observables are possible. This would be the analog (Dirac\u2019s Analogy\u00a0 Principle)of alternative compatible Poisson structures invariant under Classical Evolution.\u00a0<\/p>\n

Reference: <\/strong>J.F.Carinena, A.Ibort, G.Marmo, G.Morandi. Geometry from Dynamics,Classical and Quantum.\u00a0Springer, 2015<\/p>\n

David Mart\u00edn de Diego\u00a0 (ICMAT, Spain)<\/h3>\n
Title:<\/b>\u00a0Discrete mechanics and variational integrators [slides<\/a>]<\/em><\/span><\/div>\n
Abstract:\u00a0 <\/span><\/b>Among the many mathematical results obtained by Juan Carlos Marrero and his collaborators, this talk will focus on some important contributions related to discrete mechanics. In [1,2,3,4] we describe discrete Lagrangian mechanical systems on Lie groupoids, their Hamiltonian counterparts, and their extension to nonholonomic systems [5]. These constructions are relevant for the development of new geometric integrators, in particular for the numerical integration of dynamical systems with symmetry. In this talk, we review these results and discuss further developments.<\/span><\/div>\n
\u00a0<\/div>\n
References:<\/span><\/b><\/div>\n
[1] Marrero, Juan C; \u00a0Mart\u00edn de Diego, David, \u00a0Mart\u00ednez, Eduardo: \u00a0Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids. Nonlinearity 19 (2006), no. 6, 1313\u20131348.<\/span><\/div>\n
[2] Cort\u00e9s, Jorge; de Le\u00f3n, Manuel; Marrero, Juan C.; Mart\u00edn de Diego, D.; Mart\u00ednez, Eduardo: A survey of Lagrangian mechanics and control on Lie algebroids and groupoids. Int. J. Geom. Methods Mod. Phys. 3 (2006), no. 3, 509\u2013558.<\/span>
[3] \u00a0Marrero, Juan C; \u00a0Mart\u00edn de Diego, David, \u00a0Mart\u00ednez, Eduardo: The local description of discrete mechanics. \u00a0Fields Inst. Commun., 73 Springer, New York, 2015, 285\u2013317.<\/span><\/div>\n
[4] \u00a0Marrero, Juan Carlos; de Diego, David Mart\u00edn; Mart\u00ednez, Eduardo: \u00a0Local convexity for second order differential equations on a Lie algebroid. J. Geom. Mech. 13 (2021), no. 3, 477\u2013499.<\/span><\/div>\n
[5]\u00a0<\/span>Iglesias, David; Marrero, Juan C.; de Diego, David Mart\u00edn; Mart\u00ednez, Eduardo. Discrete nonholonomic Lagrangian systems on Lie groupoids. J. Nonlinear Sci. 18 (2008), no. 3, 221\u2013276.<\/span><\/div>\n
\n
\u00a0<\/div>\n
Tom Mestdag (University Antwerp, Belgium)\u00a0<\/span><\/div>\n<\/div>\n

Title<\/strong>: <\/span>The invariant inverse problem and EDS on Lie algebroids [slides<\/a>]<\/em><\/p>\n

Abstract:<\/strong> Given an invariant system of second-order ODEs on a Lie group, when does an invariant Lagrangian exist? This question is the so-called \u00abinvariant\u00bb; inverse problem. In this talk, we discuss some aspects of the problem, and we explain how it fits within the context <\/span>of exterior differential systems (EDS), once we have extended EDS theory from manifolds (and their tangent bundles) to Lie algebroids.<\/span><\/p>\n

Antonio de Nicola (University of Salerno, Italy)<\/strong><\/h3>\n

Title:<\/strong> Darboux-Lie Derivatives: a unified calculus for G-structures [slides<\/a>]<\/em><\/p>\n

Abstract:<\/strong> In the theory of G-structures on manifolds, geometric structures are often described in terms of gauge equivalence classes of soldering forms.
However, a comprehensive calculus of derivatives for such forms and their gauge transformations has been lacking. In this talk, based on joint work with
Ivan Yudin, I will introduce the concept of the Darboux-Lie derivative, a new tool designed to fill this gap.\u00a0<\/p>\n

We define the Darboux-Lie derivative for fiber bundle maps from natural bundles to associated fiber bundles. This construction generalizes the metamathematical<\/em> notion of a derivative, utilizing the Trautman lift as a very general framework. I will demonstrate how this single operator unifies various
classical concepts, showing that the standard Lie derivative, the covariant derivative, and the classical Darboux derivative for group valued maps are all
specific instances of the Darboux-Lie derivative.
Key properties of this new derivative will be discussed, including:<\/p>\n