I am an Associate Professor at the Institute of Mathematics of the Polish Academy of Sciences.

I have held postdoctoral positions at Tel Aviv University, Université Paris-Est Marne-la-Vallée (Chateaubriand Fellow), University of Cambridge and University of Oxford. I received my Ph.D. from the Hebrew University of Jerusalem under the supervision of Benjamin Weiss. I hold a M.Sc. in Mathematics from Stanford University and a B.A. in Mathematics and Physics from the Technion.

On the occasion of being awarded the 2021 National Science Centre
(Poland) Prize in Exact Sciences, I was invited to give a lecture by
the Copernicus Centre for Interdisciplinary Studies of the
Jagiellonian University.
The lecture entitled "Reconstruction of a dynamical
system from observations: A mathematical point of view" is available
here. Note that the lecture which is in English (with Polish
subtitles), is preceded by a short introduction in Polish by Dr.
Tomasz Miller and followed by a discussion in Polish.

List of Publications and Preprints Ordered by Subject

If you prefer to see the list of publications in reverse chronological order, please click here.

Mean Dimension & Universal Dynamical Embedding

Embedding $\mathbb{Z}^k$-actions in cubical shifts and $\mathbb{Z}^k$-symbolic extensions. Ergodic Theory and Dynamical Systems 31
(2011), 383–403. PDF, Journal

Mean dimension and a sharp embedding theorem: extensions of aperiodic subshifts. With Masaki Tsukamoto. Ergodic Theory and Dynamical Systems 34
(2014),1888–1896. arXiv, Journal

Mean dimension & Jaworski-type theorems. Proceedings of the London Mathematical Society, 111(4):831–850, 2015. arXivJournal

Embedding topological dynamical systems with periodic points in cubical shifts. Ergodic Theory and Dynamical Systems 37
(2017), 512–538. PDF, Journal, Corrigendum

Mean dimension of $\mathbb{Z}^k$-actions. With Elon Lindenstrauss and Masaki Tsukamoto. Geometric and Functional Analysis (2016) 26(3):778–817. arXiv, Journal

Embedding minimal dynamical systems into Hilbert cubes. With Masaki Tsukamoto. Inventiones Mathematicae 221 (2020) 113–166. arXiv, Journal

An explicit compact universal space for real flows. With Lei Jin. Journal of Differential Equations 266(6) (2019), 3438–3449. arXiv, Journal

The embedding problem in topological dynamics and Takens' theorem. With Yixiao Qiao and Gábor Szabó. Nonlinearity 31 (2018) 597–620. arXiv, Journal

Application of signal analysis to the embedding problem of $\mathbb{Z}^k$-actions. With Yixiao Qiao and Masaki Tsukamoto. Geometric and Functional Analysis 29 (2019) 1440–1502. arXiv, Journal

Mean dimension and an embedding theorem for real flows. With Lei Jin. Fundamenta Mathematicae 251 (2020), 161–181. arXiv, Journal

A Lipschitz refinement of the Bebutov-Kakutani dynamical embedding theorem. With Lei Jin and Masaki Tsukamoto. Journal of Dynamics and Differential Equations 31 (2019), 81–91. arXiv, Journal

Strongly isomorphic symbolic extensions for expansive topological flows. With Ruxi Shi. Submitted. arXiv

Mathematical Physics

Takens embedding theorem with a continuous observable. In Ergodic Theory: Advances in Dynamical Systems, pp. 134-142. Walter de Gruyter GmbH & Co KG, 2016. arXiv, Book

A probabilistic Takens theorem. With Krzysztof Barański and Adam Śpiewak. Nonlinearity 33 (2020), 4940–4966. arXiv, Journal

On the Shroer-Sauer-Ott-Yorke predictability conjecture for time-delay embeddings. With Krzysztof Barański and Adam Śpiewak. Communications in Mathematical Physics 391 (2022), no. 2, 609–641. arXiv, Journal

Prediction of dynamical systems from time-delayed measurements with self-intersections With Krzysztof Barański and Adam Śpiewak. Submitted, 2022. arXiv

Geometric Measure Theory

Regularity of almost-surely injective projections in Euclidean spaces. With Krzysztof Barański and Adam Śpiewak. Submitted, 2023. arXiv

Information Theory

Around the variational principle for metric mean dimension. With Adam Śpiewak. Studia Mathematica 261 (2021), 345–360. arXiv, Journal

Metric mean dimension and analog compression. With Adam Śpiewak. IEEE Transactions on Information Theory 66 (2020), no. 11, 6977–6998. arXiv, Journal

New uniform bounds for almost lossless analog compression. With Adam Śpiewak. 2019 IEEE International Symposium on Information Theory (ISIT), Paris, France, 2019, pp. 1702-1706. arXiv, Proceedings

Nilspaces

The structure theory of Nilspaces I. With Freddie Manners and Péter Varjú. Journal d'Analyse Mathématique 140 (2020), 299–369. arXiv, Journal

The structure theory of Nilspaces III: Inverse limit representations and topological dynamics. With Freddie Manners and Péter Varjú. Advances in Mathematics 365 (2020), 107059. arXiv, Journal

Higher order regionally proximal equivalence relations for general minimal group actions. With Eli Glasner and XiangDong Ye. Advances in Mathematics 333 (2018), 1004–1041. arXiv, Journal

Strictly ergodic distal models and a new approach to the Host-Kra factors. With Zhengxing Lian. Journal of Functional Analysis 284 (2023), no. 4, 109779. arXiv,
Journal

On the structure theory of cubespace fibrations. With Bingbing Liang. Journal of Dynamics and Differential Equations 35 (2023), 163–197.
arXiv, Journal

Maximal pronilfactors and a topological Wiener-Wintner theorem. With Zhengxing Lian. Israel Journal of Mathematics 251 (2022), 495–526. arXiv, Journal

A new short proof for the uniqueness of the universal minimal space. With Hanfeng Li.
Proceedings of the American Mathematical Society 141 (2013), 265–267. arXiv, Journal

The universal minimal space for groups of homeomorphisms
of h-homogeneous spaces. With Eli Glasner.
In Dynamical Systems and Group Actions, 105-117, Contemp. Math., 567, Amer. Math. Soc., Providence, RI, 2012. arXiv, Book

Minimal hyperspace actions of homeomorphism groups of h-homogeneous
spaces. With Eli Glasner. Journal d'Analyse Mathématique 119 (2013) , 305–332. arXivJournal

On relative extreme amenability. With Lionel Nguyen Van Thé. Scientiae Mathematicae Japonicae 28 (2015), 133–141. arXivJournal

Universal minimal flows of homeomorphism groups of high-dimensional manifolds are not metrizable. With Todor Tsankov and Andy Zucker. Mathematische Annalen 379 (2021), 1605–1622.
arXiv , Journal

Ergodic Theory

On processes which cannot be distinguished by finite observation. With Michael Hochman.
Israel Journal of Mathematics 164 (2008), 265–284. PDF, Journal

A Juzvinskiĭ addition theorem for finitely generated free group actions. With Lewis Bowen. Ergodic Theory and Dynamical Systems 34
(2014), 95–109. arXivJournal

Corrigendum to
"L. Bowen. Nonabelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii's formula.
Ergodic Theory and Dynamical Systems
30 (2010), no. 6, 1629-1663". With Lewis Bowen. Ergodic Theory Dynam. Systems 33
(2013), 643–645.

Almost sure convergence of the multiple ergodic average for certain weakly mixing systems. With Wen Huang, Song Shao and XiangDong Ye. Acta Mathematica Sinica, English Series 34 (2018), 79–90.