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.

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

English-Polish-English Mathematics Dictionaries

  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. Currently Postdoctoral Fellow at Bar-Ilan University.

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).

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
  • 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
  • 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
  • Information Theory

  • Around the variational principle for metric mean dimension.
    With Adam Śpiewak.
    To appear in Studia Mathematica, 2021.
    arXiv
  • 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.
    Submitted, 2019.
    arXiv
  • On the structure theory of cubespace fibrations.
    With Bingbing Liang.
    To appear in Journal of Dynamics and Differential Equations, 2021.
    arXiv
  • 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