Cartan and differential geometry, Lie theory, quantum groups and non commutative geometry For novel and Innovative Applications to quantum algorithms and geometric deep learning

Project Information

CaLiForNIA

Grant agreement ID: 101119552

DOI

10.3030/101119552

EC signature date 5 July 2023

Start date 1 January 2024

End date 31 December 2027

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 2 504 779,20

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

Websites, patent fillings, videos etc. (2)

Website

Creation of website

National and local public engagement events

National and local public engagementcoordination in synergy with UNIBOevents coordination

Documents, reports (1)

Recruitment

Advertisment on EURAXESS, websites,newsletters and Recruitment of PhDcandidates

Publications

Other (21)

Algorithms in 4-manifold topology

Author(s): A. Garcia-Rivas et al.
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2411.08775

Strongly invariant differential operators on parabolic geometries modelled on Gr(3,3)

Author(s): J. Slovak, V. Soucek
Publisher: Arxiv preprnt
DOI: 10.48550/ARXIV.2412.20369

BV Pushforward of Palatini-Cartan gravity

Author(s): Giovanni Canepa, Alberto S. Cattaneo
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2507.06279

Gravity Coupled with Scalar, SU(n), and Spinor Fields on Manifolds with Null-Boundary

Author(s): Alberto S. Cattaneo, Filippo Fila Robattino, Valentino Huang, Manuel Tecchiolli
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2401.09337

Levi-Civita connection on the irreducible quantum flag manifolds

Author(s): Jyotishman Bhowmick, Bappa Ghosh, Andrey O. Krutov, Réamonn Ó Buachalla
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2411.03102

Quantized semisimple Lie groups

Author(s): Fioresi, Rita; Yuncken, Robert
Published in: 2024, 2024
DOI: 10.48550/arxiv.2403.17180

Torsion-Free Bimodule Connections and the Maximal Prolongation of a First-Order Differential Calculus

Author(s): Alessandro Carotenuto, Antonio Del Dono, Réamonn Ó Buachalla, Junaid Razzaq
DOI: 10.48550/ARXIV.2512.23579

On Fundamental Theorems of Invariant Theory for the Special Linear Supergroup

Author(s): Junaid Razzaq, Rita Fioresi, Maria A. Lledo
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2504.07076

Variational noise mitigation in quantum circuits: the case of Quantum Fourier Transform

Author(s): Rafael Gómez-Lurbe, Alexander Bernal, Armando Pérez, Bryan Zaldívar, J. Alberto Casas
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2511.05274

Controlled Generation with Equivariant Variational Flow Matching

Author(s): Floor Eijkelboom, Heiko Zimmermann, Sharvaree Vadgama, Erik J Bekkers, Max Welling, Christian A. Naesseth, Jan-Willem van de Meent
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2506.18340

Noncommutative Complex Structures on Quantum Homogeneous Spaces

Author(s): A. Carotenuto, R. Ó Buachalla, J. Razzaq
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2411.07767

Noncommutative complex structures for the full quantum flag manifold of Oq(SU(3))

Author(s): Alessandro Carotenuto, Réamonn Ó Buachalla, Junaid Razzaq
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2411.07767

Conformally compact and higher conformal Yang-Mills equations

Author(s): A. Rod Gover, Emanuele Latini, Andrew Waldron, Yongbing Zhang
Publisher: Arxiv Preprint
DOI: 10.48550/ARXIV.2311.11458

Graph Homomorphism Distortion: A Metric to Distinguish Them All and in the Latent Space Bind Them

Author(s): Martin Carrasco, Olga Zaghen, Kavir Sumaraj, Erik Bekkers, Bastian Rieck
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2511.03068

Geometric quantization and unitary highest weight Harish-Chandra supermodules

Author(s): Meng-Kiat Chuah, Rita Fioresi
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2405.16251

Basic quasi-reductive root data and supergroups

Author(s): Rita Fioresi, Bin Shu
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2303.18065

Surface Observables, -Knot Invariants, and Nonabelian Electric Fluxes

Author(s): Alberto S. Cattaneo
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2511.13623

Compact Quantum Homogeneous Kähler Spaces

Author(s): Biswarup Das, Réamonn Ó Buachalla, Petr Somberg
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.1910.14007

Effective normalization of sub-Riemannian connections

Author(s): Erlend Grong, Jan Slovak
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2508.00108

Quantized semisimple Lie groups

Author(s): Rita Fioresi, Robert Yuncken
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2403.17180

Variational quantum eigensolver for chemical molecules

Author(s): Luca Ion, Adam Smith
Publisher: Arxiv preprint
DOI: 10.48550/ARXIV.2512.22572

Peer reviewed articles (23)

Cartan moving frames and the data manifolds

Author(s): Eliot Tron, Rita Fioresi, Nicolas Couëllan, Stéphane Puechmorel
Published in: Information Geometry, Issue 7, 2025, ISSN 2511-2481
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S41884-024-00159-8

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

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

The geometry of quantum computing

Author(s): E. Ercolessi, R. Fioresi, T. Weber
Published in: International Journal of Geometric Methods in Modern Physics, Issue 21, 2024, ISSN 0219-8878
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S0219887824400115

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

Quantum Circuit for Imputation of Missing Data

Author(s): Claudio Sanavio, Simone Tibaldi, Edoardo Tignone, Elisa Ercolessi
Published in: IEEE Transactions on Quantum Engineering, Issue 5, 2025, ISSN 2689-1808
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.1109/TQE.2024.3447875

Three-Phase Confusion Learning

Author(s): Filippo Caleca, Simone Tibaldi, Elisa Ercolessi
Published in: Entropy, Issue 27, 2025, ISSN 1099-4300
Publisher: MDPI AG
DOI: 10.3390/E27020199

Differential Calculi on Quantum Principal Bundles Over Projective Bases

Author(s): P. Aschieri, R. Fioresi, E. Latini, T. Weber
Published in: Communications in Mathematical Physics, Issue 405, 2024, 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

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: Differential Geometry and its Applications, Issue 94, 2024, ISSN 0926-2245
Publisher: Elsevier BV
DOI: 10.1016/j.difgeo.2024.102125

Generalized root systems

Author(s): Ivan Dimitrov, Rita Fioresi
Published in: Transactions of the American Mathematical Society, Series B, Issue 11, 2024, ISSN 2330-0000
Publisher: American Mathematical Society (AMS)
DOI: 10.1090/btran/214

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

The geometry of quantum computing

Author(s): E. Ercolessi, R. Fioresi, T. Weber
Published in: International Journal of Geometric Methods in Modern Physics, Issue 21, 2024, ISSN 0219-8878
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S0219887824400115

Quantum natural gradient optimizer on noisy platforms: Quantum approximate optimization algorithm as a case study

Author(s): Federico Dell'Anna, Rafael Gómez-Lurbe, Armando Pérez, Elisa Ercolessi
Published in: Physical Review A, Issue 112, 2025, ISSN 2469-9926
Publisher: American Physical Society (APS)
DOI: 10.1103/62WX-TVK5

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

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

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

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

Author(s): M. Lapenna, A. Tsamos, F. Faglioni, R. Fioresi, F. Zanchetta, G. Bruno
Published in: Discover Applied Sciences, Issue 6, 2024, ISSN 3004-9261
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s42452-024-05985-0

Equivariant localization in Batalin-Vilkovisky formalism

Author(s): Alberto S. Cattaneo, Shuhan Jiang
Published in: Differential Geometry and its Applications, Issue 100, 2025, ISSN 0926-2245
Publisher: Elsevier BV
DOI: 10.1016/J.DIFGEO.2025.102265

Dirac quantum walk on tetrahedra

Author(s): Ugo Nzongani, Nathanaël Eon, Iván Márquez-Martín, Armando Pérez, Giuseppe Di Molfetta, Pablo Arrighi
Published in: Physical Review A, Issue 110, 2024, ISSN 2469-9926
Publisher: American Physical Society (APS)
DOI: 10.1103/PHYSREVA.110.042418

3D Supergravity in the Batalin–Vilkovisky Formalism

Author(s): A. S. Cattaneo, N. Moshayedi, A. Smailovic Funcasta
Published in: Annales Henri Poincaré, 2025, ISSN 1424-0637
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00023-025-01588-6

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

Approximate inverse measurement channel for shallow shadows

Author(s): Riccardo Cioli, Elisa Ercolessi, Matteo Ippoliti, Xhek Turkeshi, Lorenzo Piroli
Published in: Quantum, Issue 9, 2025, ISSN 2521-327X
Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
DOI: 10.22331/Q-2025-04-08-1698

Conference proceedings (3)

Sheaf Diffusion Goes Nonlinear: Enhancing GNNs with Adaptive Sheaf Laplacians

Author(s): Olga Zaghen, Antonio Longa, Steve Azzolin, Lev Telyatnikov, Andrea Passerini, Pietro Liò
Publisher: Proceedings of Machine Learning Research

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

Revisiting Random Walks for Learning on Graphs

Author(s): Jinwoo Kim, Olga Zaghen, Ayhan Suleymanzade, Youngmin Ryou, Seunghoon Hong
Publisher: ICLR 2025

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