Yonatan Gutman

Welcome to the Webpage of Yonatan Gutman

I am an Associate Professor at the Institute of Mathematics of the Polish Academy of Sciences where I head the Department of Dynamical Systems.

I am an editor at Colloquium Mathematicum. Submisstion insturctions are given under Information for Authors.

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.

Y *dot* Gutman *at* impan *dot* pl

List of publications in reverse chronological order   Google Scholar profile

  1. Leonhard Horstmeyer (2013). Part III of the Mathematical Tripos at University of Cambridge.
  2. Fanny Amyot (2014). Research M.Sc (M2) at Université Paris 6 under joint supervision with David Burguet.
  3. Adam Śpiewak (2017-2020). National Science Centre (Poland) Young Scientist.

Ph.D. students

  1. Zhengxing Lian (2018-2020). Currently Assistant Professor at Xiamen University.
  2. Bingbing Liang (2018-2020). Currently Assistant Professor at Soochow University.
  3. Ruxi Shi (2019-2021). Currently Fondation Sciences Mathématiques de Paris Postdoctoral Fellow at Sorbonne University.
  4. Adam Śpiewak (2023-2025). National Science Centre (Poland) Postdoctoral Fellow.
  5. Chunlin Liu (2024-2026).

Research Interests

I am interested in Topological Dynamics and Ergodic Theory. I am especially interested in Mean Dimension and Nilspaces.

  • What is Mean Dimension? Video
  • What are Nilspaces? Video

    • Outreach

    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.

    I am the proud author of an article at Delta.

    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.
    arXiv Journal

  • 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.
    International Mathematics Research Notices 2024 (2024), Issue 3, 2382–2419.
    arXiv, Journal

  • Local mean dimension theory for sofic group actions.
    With Felipe García-Ramos.
    To appear in Groups, Geometry, and Dynamics, 2024.
    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.
    Journal de Mathématiques Pures et Appliquées 186 (2024), 103–149.
    arXiv, Journal

  • Equivariant embedding of finite-dimensional dynamical systems
    With Michael Levin and Tom Meyerovitch.
    To appear in Mathematische Annalen, 2024.
    arXiv, Journal

  • Predicting dynamical systems with too few time-delay measurements: error estimates
    With Krzysztof Barański and Adam Śpiewak.
    Submitted, 2024.
    arXiv

    Geometric Measure Theory

  • Regularity of almost-surely injective projections in Euclidean spaces.
    With Krzysztof Barański and Adam Śpiewak.
    To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2024.
    arXiv, Journal

    • 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 II: Representation as nilmanifolds.
    With Freddie Manners and Péter Varjú.
    Transactions of the American Mathematical Society 371 (2019), 4951–4992.
    arXiv, Journal, Report in Arbeitsgemeinschaft "Limits of Structures"

  • 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

    • Universal Minimal Spaces

  • Minimal actions of homeomorphism groups.
    Fundamenta Mathematicae 198 (2008), no. 3. 191–215.
    PDF, 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.
    arXiv Journal

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

  • 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.
     arXiv Journal

  • 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.

    arXiv Journal

  • Rank as a function of measure.
    With Tomasz Downarowicz and Dawid Huczek.
    Discrete and Continuous Dynamical Systems 34 (2014), no. 7, 2741–2750.

    arXiv Journal

  • 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.

    arXiv Journal

    • English-Polish-English Mathematics Dictionaries