Publications
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
WG2
One loop effective actions in Kerr-(A)dS Black Holes
https://arxiv.org/abs/2405.13830
Paolo Arnaudo, Giulio Bonelli, Alessandro Tanzini
We compute new exact analytic expressions for one-loop scalar effective actions in Kerr (A)dS black hole (BH) backgrounds in four and five dimensions. These are computed by the connection coefficients of the Heun equation via a generalization of the Gelfand-Yaglom formalism to second-order linear ODEs with regular singularities. The expressions we find are in terms of Nekrasov-Shatashvili special functions, making explicit the analytic properties of the one-loop effective actions with respect to the gravitational parameters and the precise contributions of the quasi-normal modes. The latter arise via an associated integrable system. In particular, we prove asymptotic formulae for large angular momenta in terms of hypergeometric functions and give a precise mathematical meaning to Rindler-like region contributions. Moreover we identify the leading terms in the large distance expansion as the point particle approximation of the BH and their finite size corrections as encoding the BH tidal response. We also discuss exact properties of the thermal version of the BH effective actions. Although we focus on the real scalar field in dS-Kerr and (A)dS-Schwarzschild in four and five dimensions, similar formulae can be given for higher spin matter and radiation fields in more general gravitational backgrounds.
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
ANDREY KRUTOV AND PAVLE PANDZI C
WG3