Geometry through spectral functionals.

NCN project UMO-2020/37/B/ST1/01540

Popular description of the project in English.
Popular description of the project in Polish.

To learn more about noncommutative geometry see this page.

The project has finished.

Main results (published)

A.Bochniak, L. Dąbrowski, A. Sitarz, P. Zalecki, On geometric spectral functionals arXiv:2505.16642, sumbitted A.Bochniak, L. Dąbrowski, A. Sitarz, P. Zalecki, An impediment to torsion from spectral geometry Phys. Rev. Lett. 134, 231501 – Published 10 June, 2025 L. Dąbrowski, A. Sitarz, P. Zalecki, Spectral Torsion, Commun. Math. Phys. 405, 130 (2024) L. Dąbrowski, A. Sitarz, P. Zalecki, Spectral Metric and Einstein Functionals for Hodge-Dirac operator, J. Noncommut. Geom. (2024) A. Bochniak, A. Sitarz, Spectral interactions between strings in the Higgs background, Eur. Phys. J. Spec. Top. (2023), https://doi.org/10.1140/epjs/s11734-023-00832-6 L. Dąbrowski, A. Sitarz, P. Zalecki, Spectral Metric and Einstein Functionals, Advances in Mathematics, Vol. 427, 109128 A. Bochniak, A. Sitarz, Spectral interaction between universes, Journal of Cosmology and Astroparticle Physics 04 (2022) 055

Main talks on project results

Impediment to torsion from spectral geometry A Quantum of Noncommutativity, Ambleside (UK), 7th-11th July 2025

Spectral geometry: towards tensors and spectral evolution. Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time, CIRM, Marsille 10.4.2025

Tensors from spectral geometry invited seminar talk at the University of York, (27.03.2025)

Computing the Einstein and torsion tensors for spectral triples invited seminar talk: at Queen Mary University of London, (31.01.2025)

Geometric Spectral Functionals invited seminar talk at Charles University, Praha (12.12.2024)

Standard Model and nonproduct geometries invited seminar talk at SISSA (Trieste), (26.11.2024)

Spectral Functionals invited seminar talk at the University of Colorado, Boulder, 5.09.2024

Metric and Einstein tensors from spectral functionals Quantum Symmetries Workshop, IMPAN, 12-16.02.2024

Spectral Functionals Incontro INdAM - Cortona 2024 Noncommutative Geometry and Applications 24-28 June 2024, Cortona, Italy

Towards spectral evolution Workshop on Noncommutative and Generalized Geometry in String Theory, Gauge Theory and Related Physical Models, Corfu, September 17 - September 24, 2024

Spectral Metric and Einstein Functionals Workshop on Noncommutative and Generalized Geometry in String Theory, Gauge Theory and Related Physical Models, Corfu, September 2022

Spectral Metric and Einstein Functionals Quantum Geometry, Torshavn, June 2022

Spectral geometry and modifications of gravity. Corfu2021: Workshop on Quantum Geometry, Field Theory and Gravity 21 - 27 September 2021,

Modified bimetric gravity from spectral geometry. AlteCosmoFun Conference 2021,

Models of products of noncommutative geometries. Canadian Mathematical Society Metting 2021,

From Spectral Geometry to Bimetric Gravity. Wrocław 2021, Lukierski 80th Anniversary Conference