Ergodic group actions, characters on groups and unitary representations
This project is funded within Long-term program of support of the Ukrainian research teams at the Polish Academy of Sciences carried out in collaboration with the U.S. National Academy of Sciences with the financial support of external partners. The project period is from September 2023 to August 2025.
Principal investigator: dr hab. Artem Dudko
Team members:
dr hab. Oleksandr Danylenko, B. Verkin ILTPE, Kharkiv, Ukraine, and IM PAN
DSc Mykola Nessonov, B. Verkin ILTPE, Kharkiv, Ukraine, and IM PAN
BSc Mykyta Vieprik, V. N. Karazin KhNU, Kharkiv, Ukraine, and IM PAN
BSc Nhok Tkhai Shon Ngo, V. N. Karazin KhNU, Kharkiv, Ukraine, and IM PAN
Major events:
Simons Semester "Continued Fractions, Fractals, and Dynamics", April 27-May 31, 2026, Będlewo and Warsaw, Poland
Simons Semester "Invariant structures in groups, spaces, and algebras", January 12-February 15, 2026, Będlewo and Warsaw, Poland
Conference "Ergodic group actions and unitary representations II", June 15-19, 2025, Będlewo, Poland
UK-Poland-Ukraine trilateral meeting "Group actions and representations together with Random Matrix Theory", October 14-16, 2024, Warsaw, Poland
Conference "Ergodic group actions and unitary representations", June 16-20, 2024, Warsaw, Poland
Publications and preprints:
N.I. Nessonov and N.T.S. Ngo, Indecomposable characters of inductive limits of symmetric groups, Represent. Theory 29 (2025), pp. 256-288. doi: 10.1090/ert/689
O. I. Danylenko and M. I. Vieprik, Rank-one non-singular actions of countable groups and their odometer factors, Ergodic Theory and Dynamical Systems, 45 (2025), no. 4, pp. 1078-1128. doi:10.1017/etds.2024.69, https://arxiv.org/abs/2401.16397
M. I. Nessonov, S. D. Sinelshchikov, An analogue of the Schur-Weyl duality for the automorphisms group of a II1-factor, Journal of Lie Theory 34 (2024), No. 3, 611-638, https://arxiv.org/abs/2211.14280
T. Amrutam, A. Dudko, Y. Jiang and A. Skalski, Invariant subalgebras rigidity for von Neumann algebras of groups arising as certain semidirect products, https://arxiv.org/abs/2507.12824
A.I. Danilenko and M. Vieprik, Classification of rank-one actions via the cutting-and-stacking parameters, https://arxiv.org/abs/2504.04987
A.I. Danilenko and A. Dudko, Irreducible Koopman representations for nonsingular actions on boundaries of rooted trees, arXiv:math.DS/2503.03894
N.T.S. Ngo, Big algebra in type A for the coordinate ring of the matrix space, arxiv.org/abs/2501.04605
S. Bezuglyi, A. Dudko, and O. Karpel, Measures and dynamics on Pascal-Bratteli diagrams, arXiv:math.DS/2411.06280
A. Dudko and Y. Jiang, A character approach to the ISR property, arXiv:math.OA/2410.14517
A. Dudko and D. Gaidashev, Wild attractors for Fibonacci maps, https://arxiv.org/abs/2406.19019
A. Dudko and R. Grigorchuk, Characters and IRS's on branch groups and embeddings into hyperfinite factor, https://arxiv.org/abs/2312.13124
M.I. Nessonov, The classification of the stable factor-representations of the infinite hyperoctahedral group, https://arxiv.org/abs/2402.18058
Conferences, schools, seminars co-organized by team members with the support of the grant:
IM PAN Dynamics Systems Seminar
Conference "On geometric complexity of Julia sets VI", August 3-8, 2025, Będlewo, Poland
Conference "On geometric complexity of Julia sets V", Będlewo, Poland, June 21-26, 2024
