Lie Theory; Cartan Geometry; Quantum Groups; Integrable Systems; Vision

The results established by people involved in CaLISTA Project will give rise to publications, which will be listed in this page.

@CaLISTA authors:

- In all your works you should add the sentence
*This article/publication is based upon work from COST Action CaLISTA CA21109 supported by COST (European Cooperation in Science and Technology). www.cost.eu.*Guidelines for COST acknowledgement - Please complete the form to submit your article/publication for inclusion on this page: https://forms.gle/rVSSoU4oeMjRp9vo6

* The Geometry of Quantum Computing*https://arxiv.org/pdf/2312.14807

E. Ercolessi, R. Fioresi, T. Weber

In this expository paper we present a brief introduction to the ge-

ometrical modeling of some quantum computing problems. After a

brief introduction to establish the terminology, we focus on quantum

information geometry and ZX-calculus, establishing a connection be-

tween quantum computing questions and quantum groups, i.e. Hopf

algebras.

*WG3*

WG2https://arxiv.org/abs/2405.13830

One loop effective actions in Kerr-(A)dS Black Holes

Paolo Arnaudo, Giulio Bonelli, Alessandro Tanzini

WG2 and WG3

Rita Fioresi, Maria A. Lledo, Junaid Razzaq

**Quantum Chiral Superfields**

*We study the supersymmetric extension of the conformal symmetry and ordinary super spacetime over the complex field. The different types of superspaces can all be seen Grassmannians or flag supermanifolds (that is, sets of subspaces of a given space). We introduce non commutative coordinates in (super) spacetime in such a way that the symmetries are preserved. In order to do so, the symmetry (super) group become also non commutative space or 'quantum group'.*

WG1

Johnson Allen Kessy, Dennis The

**On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class**

*A well-known classical result due to Sophus Lie is the classification of scalar ODEs with maximal and submaximal symmetry. Proving analogous results for vector ODEs in fully generality is not feasible using Lie-theoretic techniques. Instead, Cartan geometric and representation-theoretic tools are used to completely resolve the problem for vector ODEs in the so-called C-class.*

Rita Fioresi, Bin Shu

**Basic quasi-reductive root data and supergroups**

Nathan Couchet, Robert Yuncken

**A groupoid approach to the Wodzicki residue**

Vladislav G. Kupriyanov, Alexey A. Sharapov, Richard J. Szabo

**Symplectic Groupoids and Poisson Electrodynamics**

Keegan J. Flood, Mauro Mantegazza, Henrik Winther

**Symbols in Noncommutative Geometry**

R. Fioresi, A. Marraffa, J. Petkovic

**A new perspective on border completion in visual cortex as bicycle rear wheel geodesics paths via sub-Riemannian Hamiltonian formalism**

* ON RELATIVE TRACTOR BUNDLES*https://arxiv.org/pdf/2405.13614

ANDREAS CAP, ZHANGWEN GUO, AND MICHAL WASILEWICZ

This article contributes to the relative BGG-machinery for para-

bolic geometries. Starting from a relative tractor bundle, this machinery con-

structs a sequence of differential operators that are naturally associated to the

geometry in question. In many situations of interest, it is known that this se-

quence provides a resolution of a sheaf that can locally be realized as a pullback

from a local leaf space of a foliation that is naturally available in this situation.

An explicit description of the latter sheaf was only available under much more

restrictive assumptions.

WG1

Indranil Biswas, Benjamin McKay

**Locally homogeneous holomorphic geometric structures on Moishezon manifolds**

R. Fioresi, F. Zanchetta

**Deep Learning and Geometric Deep Learning: an introduction for mathematicians and physicists**

Laurenţiu Bubuianu, Douglas Singleton, Sergiu. I. Vacaru

**Nonassociative black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics**

P. Aschieri, R. Fioresi, E. Latini, T. Weber

**Differential Calculi on Quantum Principal Bundles over Projective Bases**

WG3

Milagrosa Aldana, María A. Lledó

**The fuzzy bit**

*In this paper we revise the idea of appliying fuzzy sets to quantum theory. It is established that, appropriately using a particular Universe of discourse, Quantum Mechanics can be expressed as a theory of fuzzy sets, according to a result by Pycakz for quantum logics in general.*

DOI: https://doi.org/10.3390/sym15122103

on *Simmetry* vol. 15 year 2023

**Reduction of Quantum Principal Bundles over non affine bases**

Rita Fioresi, Emanuele Latini, Chiara Pagani

https://arxiv.org/html/2403.06830v1

WG3

**QUANTISED sl2-DIFFERENTIAL**** ALGEBRAS**https://arxiv.org/pdf/2403.08521