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

Ph.D. students

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 Dynam. Systems 31 (2011), 383–403.
    PDF, Journal
  • Mean dimension and a sharp embedding theorem: extensions of aperiodic subshifts.
    With Masaki Tsukamoto.
    Ergodic Theory Dynam. 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 Dynam. Systems 37 (2017), 512–538.
    PDF, Journal
  • Mean dimension of $\mathbb{Z}^k$-actions.
    With Elon Lindenstrauss and Masaki Tsukamoto.
    Geom. Funct. Anal. (2016) 26(3):778–817.
    arXiv, Journal
  • Embedding minimal dynamical systems into Hilbert cubes.
    With Masaki Tsukamoto.
    Submitted, 2017.
    arXiv
  • 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.
    Submitted, 2017.
    arXiv
  • Mean dimension and an embedding theorem for real flows.
    With Lei Jin.
    To be published in Fundamenta Mathematicae, 2019.
    arXiv
  • A Lipschitz refinement of the Bebutov-Kakutani dynamical embedding theorem.
    With Lei Jin and Masaki Tsukamoto.
    To be published in the Journal of Dynamics and Differential Equations, 2018.
    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.
    Submitted, 2019.
    arXiv
  • Information Theory

  • Metric mean dimension and analog compression.
    With Adam Śpiewak.
    Submitted, 2019.
    arXiv
  • Nilspaces

  • The structure theory of Nilspaces I.
    With Freddie Manners and Péter Varjú.
    To appear in Journal d'Analyse Mathématique, 2018.
    arXiv
  • The structure theory of Nilspaces II: Representation as nilmanifolds.
    With Freddie Manners and Péter Varjú.
    To appear in Transactions of the American Mathematical Society, 2018.
    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.
    Submitted, 2016.
    arXiv
  • 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
  • Universal Minimal Spaces

  • Minimal actions of homeomorphism groups.
    Fund. Math. 198 (2008), no. 3. 191–215.
    PDF, Journal 
  • A new short proof for the uniqueness of the universal minimal space.
    With Hanfeng Li.
    Proc. Amer. Math. Soc. 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.
    J. Anal. Math. 119 (2013) , 305–332.
    arXiv Journal
  • On relative extreme amenability.
    With Lionel Nguyen Van Thé
    Sci. Math. Jpn. 28 (2015), 133–141.
    arXiv Journal
  • Ergodic Theory

  • On processes which cannot be distinguished by finite observation.
    With Michael Hochman.
    Israel J. Math. 164 (2008), 265–284.

    PDF, Journal
  • A Juzvinskiĭ addition theorem for finitely generated free group actions.
    With Lewis Bowen.
    Ergodic Theory Dynam. 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 Dynam. 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 Contin. Dyn. Syst. 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. Math. Sin.-English Ser. 34 (2018), 79–90.
    arXiv Journal