Reconstruction of Lie groupoids from their corresponding operator algebras

2025 - 2027

Grant of the Ministry of Research, Innovation and Digitization, CNCS–UEFISCDI, project number PN-IV-P1-PCE-2023-0264

Research team:

Daniel Beltita (principal investigator)
Ingrid Beltita
Sebastian Burciu
Radu Purice
Bogdan Udrea

1st year (2025): Abstract harmonic analysis on groupoids with applications to reconstruction problems

Deliverables:

I. Beltita, D. Beltita, Invariant Hilbert spaces of distribution vectors in Lie group representations. Arkiv för matematik (to appear).

(See preprint arXiv: 2507.05988 [math.RT].)

I. Beltita, D. Beltita, On the C*-algebras of linear dynamical systems. Preprint arXiv: 2511.20638 [math.OA].
S. Burciu, On some integral properties of dimensions in Isaacs fusion cateories. Preprint arXiv: 2507.07329 [math.QA].
H.D. Cornean, B. Helffer, R. Purice, A rigorous Peierls-Onsager effective dynamics for semimetals in long-range magnetic fields. Preprint arXiv: 2411.14171 [math-ph].

Dissemination:

R. Purice: Analysis Seminar of the Department of Mathematical Sciences, Aalborg University, 22 January 2025, Aalborg, Denmark.
R. Purice: Twisted pseudodifferential calculus and a general rigorous form of the Peierls--Onsager substitution. Series of 5 presentations in the seminar Operator Theory, Institute of Mathematics "Simion Stoilow" of the Romanian Academy, 30 January - 27 February 2025, Bucharest, Romania, and online.
D. Beltita: On the integrability of transitive Lie algebroids. Prague-Hradec Kralove Seminar: Cohomology in algebra, geometry, physics and statistics, 19 February 2025, Institute of Mathematics, Czech Academy of Sciences, Prague, online.
D. Beltita: Intrinsic symmetry of von Neumann algebras. Seminario "Mischa Cotlar", 6 June 2025, Instituto Argentino de Matemática "Alberto P. Calderón" (IAM-CONICET), Buenos Aires, online.
I. Beltita: Pedersen multipliers for Banach space representations of nilpotent Lie groups. International Conference on Analysis, the 16th Romanian-Finnish Seminar, 24 - 27 June 2025, University of Alba Iulia, Romania.
D. Beltita: A groupoid picture of standard forms of W*-algebras. Forschungsseminar Lie-Gruppen, 30 June 2025, Friedrich-Alexander-Unversität Erlangen-Nürnberg, Department Mathematik, Erlangen, Germany.
I. Beltita: Square integrable representations of solvable Lie groups. International Workshop on Operator Theory and Its Applications (IWOTA), 14 - 18 July 2025, University of Twente, Netherlands.
D. Beltita: One-parameter operator groups on Hardy spaces. 7th Summer Workshop on Operator Theory, 21 - 24 July 2025, University of Agriculture in Kraków, Poland.
I. Beltita: C*-rigidity of the Heisenberg group. Conference "Women in Harmonic Analysis", 8 - 10 September 2025, University of Paderborn, Germany.

Foreign collaboration activities:

H. Cornean (University of Aalborg, Denmark) and B. Helffer (Nantes Université, France), collaboration with R. Purice
F. Pelletier (University of Savoie Mont Blanc, France), 21-28 May 2025, research visit by D. Beltita.
K.-H. Neeb (University of Erlangen-Nürnberg, Germany), 29 June - 5 July 2025, research visit by D. Beltita.
U. Enstad (University of Oslo, Norway), 5-10 October 2025, research visit to IMAR.
J. E. Galé (University of Zaragoza, Spain), 18-25 October 2025, research visit to IMAR.
F. Pelletier (University of Savoie Mont Blanc, France), 2-8 November 2025, research visit by D. Beltita.
J. T. van Velthoven (University of Vienna, Austria), 10-15 November 2025, research visit to IMAR.
A. Dobrogowska (University of Bialystok, Poland), 23-30 November 2025, research visit to IMAR.
G. Jakimowicz (University of Bialystok, Poland), 23-30 November 2025, research visit to IMAR.

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