Cartan geometry, Lie and representation theory, Integrable Systems, quantum Groups and quantum computing towards the understanding of the geometry of deep Learning and its Applications

Project Information

CaLIGOLA

Grant agreement ID: 101086123

DOI

10.3030/101086123

EC signature date 3 November 2022

Start date 1 January 2023

End date 31 December 2026

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 874 000,00

Coordinated by

ALMA MATER STUDIORUM - UNIVERSITA DI BOLOGNA
Italy

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Deliverables

Documents, reports (10)

D2.1 classification of integrable systems

Preprint on the classification of Integrable systems

D3.3 quantum symmetric spaces

Volume of Proceedings of a quantum symmetric spaces conferences

D1.3, D1.4 Kahler supergeometry

Preprint on Kahler supergeometry 1 UNIBO Research Specialist 24D1.4Proceedings of a conference on Cartan Geometry and Representation theory

D5.1, D5.4 Models of vision

Preprint: New models of vision inspired by Lie group thermodynamics.Proceedings of a meeting organized by Thales on information geometry

D2.2 SUSY gauge fields theories

Preprint on SUSY gauge field theories

D1.1, D1.2: BGG and subriemannian geometry

Preprint on BGG operatorsPreprint on subriemannian geometry

D4.1 Quantum information theory

Preprint: Quantum Geometric Tensor, Quantum Information theory

D4.2 Topological Quantum Computation

Preprint: Topological Quantum Computation and Yetter-Drinfel'd modules

D3.1, D3.2 Spectral triples for quantum flag manifolds.

Preprint on Spectral triples for quantum flag manifolds.Preprint on Quantum flag manifolds

D5.2,D5.3 Geometric deep learning

Preprint on Geneos.Preprint: Geometric Deep Learning and quantum differential calculus.

Data Management Plan (1)

D6.4 Data management plan

Data management plan

Websites, patent fillings, videos etc. (2)

D6.3 Public engagement

National and local public engagement events coordination

D6.1, D6.2 Dissemination plan

Website creation and newsletter deliveryCoordination of dissemination activities

Publications

Peer reviewed articles (31)

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

Author(s): R. Fioresi; A. Marraffa; J. Petkovic
Published in: Diff. Geom. and Applications, 2024
Publisher: Elsevier
DOI: 10.48550/ARXIV.2304.00084

Black hole perturbation theory and multiple polylogarithms

Author(s): Gleb Aminov, Paolo Arnaudo, Giulio Bonelli, Alba Grassi, Alessandro Tanzini
Published in: Journal of High Energy Physics, Issue 2023, 2024, ISSN 1029-8479
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/JHEP11(2023)059

Semiholonomic jets and induced modules in Cartan geometry calculus

Author(s): Jan Slovák, Vladimír Souček
Published in: Archivum Mathematicum, 2024, ISSN 0044-8753
Publisher: Masaryk University Press
DOI: 10.5817/AM2024-4-191

The Geometry of Quantum Computing

Author(s): E. Ercolessi, R. Fioresi, T. Weber
Published in: Int. J. of Geometric Methods in Mod. Phys., 2024
Publisher: World Scientific Publishing
DOI: 10.48550/arXiv.2312.14807

Deep learning and geometric deep learning: An introduction for mathematicians and physicists

Author(s): R. Fioresi, F. Zanchetta
Published in: International Journal of Geometric Methods in Modern Physics, Issue 20, 2023, ISSN 0219-8878
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S0219887823300064

Gene selection for prediction of transcriptome signal based on a machine learning approach

Author(s): Pietro Demurtas, Jacopo Bertozzi, Irene Di Silvestro, Kevin Carlin, Andre Ghetti, Brian Krause, Giovanni Perini, Ferdinando Zanchetta, Rita Fioresi
Published in: Discover Applied Sciences, Issue 7, 2025, ISSN 3004-9261
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S42452-025-07841-1

One loop effective actions in Kerr-(A)dS black holes

Author(s): Paolo Arnaudo, Giulio Bonelli, Alessandro Tanzini
Published in: Physical Review D, Issue 110, 2024, ISSN 2470-0010
Publisher: American Physical Society (APS)
DOI: 10.1103/PHYSREVD.110.106006

The Fuzzy Bit

Author(s): Milagrosa Aldana; María Antonia Lledó
Published in: Symmetry, Vol 15, Iss 12, p 2103 (2023), 2023
Publisher: CORNELL UNIVERSITY
DOI: 10.48550/ARXIV.2311.14083

Boundary Structure of the Standard Model Coupled to Gravity

Author(s): Giovanni Canepa, Alberto S. Cattaneo, Filippo Fila-Robattino, Manuel Tecchiolli
Published in: Annales Henri Poincaré, 2024, ISSN 1424-0637
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00023-024-01485-4

Temperature-based pruning for input features in Graph Neural Networks

Author(s): Lapenna Michela, Faglioni Francesco, Fioresi Rita, Bruno Giovanni
Published in: The European Physical Journal Plus, Issue 140, 2025, ISSN 2190-5444
Publisher: Springer Science and Business Media LLC
DOI: 10.1140/EPJP/S13360-025-06804-0

Black Hole Perturbation Theory Meets CFT$_2$: Kerr Compton Amplitudes from Nekrasov-Shatashvili Functions

Author(s): Bautista, Yilber Fabian; Bonelli, Giulio; Iossa, Cristoforo; Tanzini, Alessandro; Zhou, Zihan
Published in: Phys. Rev. D, Issue 109, 2024
Publisher: APS
DOI: 10.48550/ARXIV.2312.05965

On the Đurđević approach to quantum principal bundles

Author(s): Antonio Del Donno, Emanuele Latini, Thomas Weber
Published in: Journal of Geometry and Physics, Issue 216, 2025, ISSN 0393-0440
Publisher: Elsevier BV
DOI: 10.1016/J.GEOMPHYS.2025.105567

Spontaneous Emergence of Robustness to Light Variation in CNNs With a Precortically Inspired Module

Author(s): J. Petkovic, R. Fioresi
Published in: Neural Computation, Issue 36, 2024, ISSN 0899-7667
Publisher: MIT Press
DOI: 10.1162/NECO_A_01691

Gene selection for prediction of transcriptome signal based on a machine learning approach

Author(s): Pietro Demurtas, Jacopo Bertozzi, Irene Di Silvestro, Kevin Carlin, Andre Ghetti, Brian Krause, Giovanni Perini, Ferdinando Zanchetta, Rita Fioresi
Published in: Discover Applied Sciences, ISSN 3004-9261
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S42452-025-07841-1

Geometric deep learning for enhanced quantitative analysis of microstructures in X-ray computed tomography data

Author(s): Lapenna M.; Tsamos A.; Faglioni F.; Fioresi R.; Zanchetta F.; Bruno G.
Published in: Discover Applied Sciences, 2024
Publisher: SPRINGER NATURE
DOI: 10.1007/S42452-024-05985-0

Cartan moving frames and the data manifolds

Author(s): Eliot Tron, Rita Fioresi, Nicolas Couëllan, Stéphane Puechmorel
Published in: Information Geometry, Issue 7, 2024, ISSN 2511-2481
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S41884-024-00159-8

Reducing the number of qubits by a half in one dimensional quantum simulations of Ising chains

Author(s): Mehrabankar, Somayeh; Garca-March, Miguel ngel; Almudver, Carmen G.; Prez, Armando
Published in: New Journal of Physics, 2024
Publisher: New Journal of Physics, Volume 26, August 2024
DOI: 10.48550/arxiv.2308.01545

Kolmogorov–Arnold and Long Short-Term Memory Convolutional Network Models for Supervised Quality Recognition of Photoplethysmogram Signals

Author(s): Aneeqa Mehrab, Michela Lapenna, Ferdinando Zanchetta, Angelica Simonetti, Giovanni Faglioni, Andrea Malagoli, Rita Fioresi
Published in: Entropy, Issue 27, 2025, ISSN 1099-4300
Publisher: MDPI AG
DOI: 10.3390/E27040326

Noncommutative complex structures for the full quantum flag manifold of $$\mathcal {O}_q(\textrm{SU}_3)$$

Author(s): Alessandro Carotenuto, Réamonn Ó Buachalla, Junaid Razzaq
Published in: Letters in Mathematical Physics, Issue 115, 2025, ISSN 1573-0530
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S11005-025-01955-8

Harmonic analysis of compact Lie supergroups

Author(s): M.-K. Chuah, C.A. Cremonini, R. Fioresi
Published in: Expositiones Mathematicae, Issue 43, 2025, ISSN 0723-0869
Publisher: Elsevier BV
DOI: 10.1016/J.EXMATH.2024.125586

Communications in Mathematical Physics

Author(s): P. Aschieri, R. Fioresi, E. Latini, T. Weber
Published in: Communications in Mathematical Physics, Issue 405, ISSN 0010-3616
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00220-024-05007-5

Equivariant BV-BFV formalism

Author(s): Alberto S. Cattaneo, Nima Moshayedi
Published in: Journal of Geometry and Physics, Issue 218, 2026, ISSN 0393-0440
Publisher: Elsevier BV
DOI: 10.1016/J.GEOMPHYS.2025.105684

Thermodynamics modeling of deep learning systems for a temperature based filter pruning technique

Author(s): Lapenna, M; Faglioni, F; Fioresi, R
Published in: Frontiers in Physics, Vol 11 (2023), 2023
Publisher: FRONTIERS
DOI: 10.3389/FPHY.2023.1145156

Noncommutative differential geometry on crossed product algebras

Author(s): Andrea Sciandra; Thomas Weber
Published in: Journal of Algebra, 2025
Publisher: CORNELL UNIVERSITY
DOI: 10.48550/ARXIV.2308.14662

Solitons in a photonic nonlinear quantum walk: lessons from the continuum

Author(s): Anglés-Castillo, Andreu; Pérez, Armando; Roldán, Eugenio
Published in: 2023
Publisher: CORNELL UNIVERSITY
DOI: 10.48550/ARXIV.2308.01014

Effect of noisy environment on secure quantum teleportation of unimodal Gaussian states

Author(s): Mehrabankar, S.; Mahmoudi, P. (Payman); Abbasnezhad, F.; Afshar, D.; Isar, A.
Published in: Quantum Information Processing, 2024
Publisher: Springer Nature
DOI: 10.1007/s11128-024-04545-0

Basic quasi-reductive root data and supergroups

Author(s): Fioresi, Rita; Shu, Bin
Published in: 2023
Publisher: CORNELL UNIVERSITY
DOI: 10.48550/ARXIV.2303.18065

Chamfer distance for non-linear registration of Triply Periodic Minimal Surface lattices

Author(s): Michela Lapenna, Francesco Faglioni, Keerthana Chand, Bardia Hejazi, Rita Fioresi, Giovanni Bruno
Published in: Additive Manufacturing Letters, Issue 14, 2026, ISSN 2772-3690
Publisher: Elsevier BV
DOI: 10.1016/J.ADDLET.2025.100299

Lusztig's positive root vectors and a Dolbeault complex for the A-series full quantum flag manifolds

Author(s): Réamonn Ó Buachalla, Petr Somberg
Published in: Journal of Algebra, Issue 678, 2025, ISSN 0021-8693
Publisher: Elsevier BV
DOI: 10.1016/J.JALGEBRA.2025.03.035

Generalized root systems

Author(s): Dimitrov, Ivan; Fioresi, Rita
Published in: Transactions of the AMS, 2023
Publisher: AMS
DOI: 10.48550/ARXIV.2308.06852

A novel iterative algorithm to improve segmentations with deep convolutional neural networks trained with synthetic X-ray computed tomography data (i.S.Sy.Da.T.A)

Author(s): A. Tsamos, S. Evsevleev, R. Fioresi, F. Faglioni, G. Bruno
Published in: Computational Materials Science, Issue 223, 2024, ISSN 0927-0256
Publisher: Elsevier BV
DOI: 10.1016/J.COMMATSCI.2023.112112

Other (2)

Levi-Civita connection on the irreducible quantum flag manifolds

Author(s): J. Bhowmick, B. Ghosh, A. Krutov, R. Buachalla
Published in: 2024
Publisher: arxiv
DOI: 10.48550/arXiv.2411.03102

CONFORMALLY COMPACT AND HIGHER CONFORMAL YANG–MILLS EQUATIONS

Author(s): A. Rod Gover, Emanuele Latini, Andrew Waldron, Yongbing Zhang
Published in: 2024

Conference proceedings (1)

Gauge transformations on quantum principal bundles

Author(s): Thomas Weber, Antonio Del Donno, Emanuele Latini
Published in: "Proceedings of Proceedings of the Corfu Summer Institute 2024 ""School and Workshops on Elementary Particle Physics and Gravity"" — PoS(CORFU2024)", 2025
Publisher: Sissa Medialab
DOI: 10.22323/1.490.0310

Monographic books (1)

Geometric Science of Information

Published in: Lecture Notes in Computer Science, 2023
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0

Book chapters (1)

Enhancing CNNs Robustness to Occlusions with Bioinspired Filters for Border Completion

Author(s): Catarina P. Coutinho, Aneeqa Merhab, Janko Petkovic, Ferdinando Zanchetta, Rita Fioresi
Published in: Lecture Notes in Computer Science, Geometric Science of Information, 2025
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-03918-7_28