GEOMETRY AND DYNAMICS

14 Jan 2026, 10:00 → 16 Jan 2026, 14:00 Europe/Rome

Aula Magna (Sede delle Accademie Napoletane)

 

The workshop aims to bring together experts working in various fields related to recent developments in classical and quantum geometry in physics. On this occasion, we will be glad to celebrate Beppe Marmo's 80th birthday upon discussing these themes with him, his students, collaborators, and friends.

For organizational reasons, registration is free but mandatory. Please register via the web form. Talks are on invitation only.

The list of speakers and the workshop timetable are now available. We are looking forward to welcoming you in Naples!

Following Online

The conference can be followed online via Microsoft Teams. Access is provided through this link. Please connect to the Microsoft Teams platform, and follow the on-screen instructions. To join the conference Team use the password: uagirt1

 

Local Organizing Committee

Paolo Aniello, Giuseppe Bimonte, Salvatore Capozziello, Goffredo Chirco, Alioscia Hamma, Giampiero Esposito, Maxim Kurkov, Fedele Lizzi, Guido Russo, Luca Schiavone, Guido Trombetti, Patrizia Vitale, Alessandro Zampini

Wednesday 14 January

10:15 Opening

10:30 coffee break

Wednesday 14 - morning

1 The cosmological past lightcone, FLRW symmetries, and Dark Energy

Abstract:
We illustrate a non-perturbative technique that allows the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) observer to evaluate a measurable, scale-dependent distance functional between her idealized FLRW past light cone and the actual physical past light cone. This distance functional quantifies the FLRW symmetry-breaking in regions of spacetime where structure formation dominates the cosmological landscape. From the point of view of the FLRW observer, gathering data from sources at cosmological redshift z, this functional generates a scale-dependent contribution that strongly erodes the interpretation of the FLRW cosmological constant as representing dark energy.

Speaker: Mauro Carfora

2 Gauge invariance and quantum information

Abstract:
We analyse how the interplay between entanglement and quantum magic
constrains the structure of fundamental interactions, We show that the
entanglement generated by the scattering of gluons and gravitons is
maximal if the couplings preserve gauge invariance and diffeomorfism
invariance. Under the same conditions quantum magic, i.e. the
non-Clifford component that enables universal quantum computation is
minimal, but never vanishes. This dual informational principle may
underlie the emergence of gauge invariance in fundamental physics.

Speaker: Manuel Asorey

3 The Geometric Phase and the Spin-Statistics Theorem

Abstract:
The spin-statistics theorem has a long history and has been proved under a variety of assumptions. However, the consensus is that we do not yet understand the spin-statistics connection in its most intuitive and elementary form. In this work, we try to fill this gap by giving an intuitive, topological proof based on the idea that the histories of spinning elementary particles can be modeled as ribbons. This idea is then shown to emerge from group theoretical and geometric considerations based on Poincare symmetry and co-adjoint orbits.The geometric phase plays a natural role in these considerations.

Speaker: Joseph Samuel

12:30 lunch break

Wednesday 14 - afternoon

4 Kitaev models for discrete groups

Abstract:
We will present the geometrical and algebraic structure of Kitaev models with both abelian and non-abelian discrete gauge group.

Speaker: Elisa Ercolessi

5 Quantum Measure in Regge Calculus

Abstract:
In a recent paper, A. D’Adda has shown that assigning a length to each link and coordinates to each labelled vertex it is possible to fix a non-Euclidean flat metric and a reference frame in each simplex invariant under GL(n,R). The metric tensor is function of the link lengths and of the coordinates of the vertices. We will show that by performing a gauge-fixing on the metric tensor, we can succeed in calculating the Fadeev-Popov determinant for the Quantum Measure of the Regge Calculus. This has been a longstanding problem that we hope to contribute to understand. This could have important consequences for numerical simulations of Quantum Regge Calculus and for Dynamical Triangulations and, probably, for Causal Dynamical Triangulations.
D’Adda has shown that by assigning a length to each link and coordinates to each labelled vertex, one can define a non-Euclidean flat metric and a reference frame within each simplex that is invariant under . In this formulation, the metric tensor is a function of both the link lengths and the vertex coordinates.
In this talk, we show that by performing an appropriate gauge fixing of the metric tensor, it is possible to compute explicitly the Faddeev–Popov determinant entering the quantum measure of Regge calculus. The determination of this measure has been a longstanding open problem, and our results represent a step toward its resolution.
A well-defined quantum measure has important implications for numerical investigations of quantum gravity. In particular, our approach may lead to improved simulations in Quantum Regge Calculus and could also have consequences for Dynamical Triangulations and, potentially, for Causal Dynamical Triangulations.

Speaker: Gabriele Gionti

6 Dynamics from Geometry in Stokes Flow

Abstract:
Particle-laden flows are everywhere: a fluid carries a dispersed population of small rigid bodies whose shapes can be as simple as spheres or as intricate as helices. This talk asks a basic question at the interface of geometry and dynamics. In the limit where inertia is negligible (Re → 0), can the shape of a particle, together with a time-dependent forcing that averages to zero, produce a net transport of the particles through the fluid, and can this transport distinguish between left- and right-handed (enantiomeric) shapes?

At zero Reynolds number, the governing equations are linear and kinematically reversible, so motion cannot rely on inertia or "memory" in the usual sense. Net effects must instead come from broken symmetries and from the geometry of the path traced by the system through its configuration space, for rigid bodies the space of orientations is the rotation group. This viewpoint echoes an old theme in physics. Einstein’s early work on suspensions already showed how macroscopic observables, such as effective viscosity, encode microscopic structure even in the simplest dilute limit [1]. The challenge is that for genuinely three-dimensional shapes, the microscopic response to the local flow is hard to compute at the scale needed to study collective transport in suspensions.

I will present a multiscale route around this bottleneck [2]: a neural surrogate closure that learns the geometry-dependent single-particle response to local linear Stokes flow (including stress and rotational couplings, and chirality-sensitive contributions for helices). The result is a shape-agnostic building block designed to be embedded into suspension-level solvers, enabling systematic studies of geometry-induced pumping and enantioselective transport once the coupling is in place. The goal of the talk is to frame the fundamental physics problem clearly, and to show how modern surrogate modelling makes it tractable without giving up geometric fidelity.

[1] Einstein, A. (1906). A new determination of molecular dimensions. Annln., Phys., 19, 289-306.
[2] Laudato, M. (2025). Neural-Network Closures for Complex-Shaped Particles in the Force-Coupling Method. arXiv preprint arXiv:2512.14532.

Speaker: Marco Laudato

16:00 coffee break

Wednesday 14 - afternoon

7 Defining hybrid quantum-classical ensembles

Abstract:
We present a brief summary of the different geometric tools that we developed over the last 15 years to model hybrid quantum-classical systems. Usually obtained as an approximation of an initially full quantum model where two different mass or time scales exist, these models offer a very useful framework for numerical simulations of molecular systems. We will review the geometrical formulation of the dynamics of such systems and their use in the context of hybrid quantum-classical statistical mechanics.

Speaker: Jesus Clemente-Gallardo

8 TBA

Speaker: Fernando Falceto

Thursday 15 January

Thursday 15 - morning

9 Dialogo con Beppe su cose passate

Speaker: Franco Magri

10 Field strengths in Poisson Electrodynamics

Abstract:
In recent years a novel approach towards the understanding of the behavior of gauge symmetries in the presence of noncommutativity has been introduced under the name of Poisson Gauge Theories. Within this framework several results have been obtained in the case of U(1) gauge symmetry, i.e., Poisson Electrodynamics. Interestingly, the geometric framework emerging from the above-mentioned results appears to be that of symplectic groupoids and symplectic realizations. In this talk I will present this geometric framework and show the relation existing among the different notions of field strengths that have been considered so far. Joint work with P. Vitale and V. Kupriyanov

Speaker: Fabio Di Cosmo

10:30 coffee break

Thursday 15 - morning

11 TBA

Speaker: Saverio Pascazio

12 TBA

Speaker: Luigi Martina

13 Looking at entanglement through the lens of algebraic geometry

Abstract:
We aim to show that algebraic geometry provides a powerful and natural framework for exploring diverse aspects of entanglement. By employing tools such as secant varieties and multilinear ranks, we obtain a detailed classification of entanglement under stochastic local operations and classical communication in multipartite systems.
In addition, we advocate the use of embeddings—from Veronese to Segre–Veronese—to construct relevant entanglement subspaces within the Hilbert space of a multipartite system.

Speaker: Stefano Mancini

12:30 lunch break

Thursday 15 - afternoon

14 TBA

Speaker: Dariusz Chruściński

15 Beyond the boundary: Unfolding hidden unitarity

Abstract:
Hermitian operators that fail to be self-adjoint are ubiquitous in quantum mechanics, from boundary-value problems and singular interactions to effective descriptions of open systems. Their non-self-adjointness is often interpreted as a fundamental loss of unitarity or reversibility. Building on Naimark’s dilation theorem, I will show how non-unitarity emerges from the folding and projection of unitary dynamics onto an incomplete domain. The resulting picture reveals non-self-adjoint observables as shadows of an underlying unitary structure.

Speaker: Paolo Facchi

16 An invitation to quantum reference frames: the perspective-neutral way

Abstract:
In standard textbook treatments, reference frames serve merely to describe physical situations and are taken to be external to the systems under study. Yet many physically relevant settings — such as those encountered in gauge theories, gravity, or quantum communication — lack any meaningful external frame. This raises the question of how to describe physics in the absence of such a structure.

The answer lies in adopting internal reference frames: subsystems that transform non-trivially under the symmetry group of interest and provide the means to describe physical systems “from the inside” in purely relational terms. This perspective embodies the idea that all reference frames are associated with physical systems and are therefore ultimately quantum — so-called quantum reference frames (QRFs). QRFs are thus essential for describing and extracting physics whenever no external reference frame for a given symmetry group is available. This situation arises most prominently for gauge symmetries, as in gauge theory and gravity, where QRFs appear naturally in the construction of physical observables and in the definition of a relational notion of locality and gauge-invariant subsystems. The choice of an internal QRF is typically non-unique, leading to a novel notion of quantum covariance of physical properties under QRF transformations.

In this talk, I’ll review the basic ideas and tools of the QRF program, with particular emphasis on the so-called perspective-neutral framework for quantum frame covariance. I will conclude by discussing recent developments and some open questions in this broad and active area of research.

Speaker: Fabio Mele

16:30 coffee break

17:00 online contributions

Friday 16 January

Fryday 16

17 TBA

Speaker: Juan Manuel Perez-Pardo

18 Look: it's GNS Hilbert spaces everywhere! Information geometry via the GNS construction

Abstract:
Many of the standard Riemannian structures in information geometry arise from a single source: the Hilbert space provided by the Gelfand-Naimark-Segal (GNS) construction for states on a C*-algebra. I will explain how the Fisher-Rao metric (classical models), the Fubini-Study/quantum geometric tensor (pure quantum states), and the Bures-Helstrom metric (faithful quantum states in finite dimensions) can all be obtained as pullbacks of the same GNS-induced geometry along a statistical model. The same viewpoint naturally yields an associated 2-form that vanishes in the commutative case, reduces to the standard Berry curvature/symplectic form for pure quantum states, and measures the commutativity of symmetric logarithmic derivatives for faithful quantum states in finite dimensions.

Speaker: Florio Maria Ciaglia

11:00 coffee break

Fryday 16

19 Exceptional Points Manifolds in Quantum Open Systems

Abstract:
We study Liouvillian exceptional points (LEPs) of quantum open systems, focusing on their emergence and structure in both continuous Lindbladian dynamics and discrete-time quantum circuits. Using an analytically solvable two-qubit model, we characterize LEPs manifolds and the associated bifurcations in parameter space. We show that LEPs persist in discrete brickwork completely positive trace-preserving (CPTP) circuits, retaining their characteristic non-Hermitian sensitivity. Our results establish a bridge between continuous open-system dynamics and stroboscopic quantum-circuit architectures, with implications for exceptional-point-based quantum sensing.

Speaker: Mario Salerno

20 Elementary particles on curved space-times

Abstract:
A symmetry based notion of elementary particles on curved space-times is presented where the Poincaré group of Minkowski space-time is replaced by a canonical groupoid. The irreducible projective representations of such groupoid, called the Wigner groupoid of the given space-time, provide a natural notion of elementary particles valid on any space-time. The computation of such representations for a large class of space-times recovers Wigner’s original classification of elementary particles on flat space-time with a surprise: there is a new family of representations parametrized by magnetic momentum like quantity.

Speaker: Alberto Ibort

13:00 lunch at Accademia