Mariusz Mirek

University of Wrocław
Mathematical Institute
Plac Grunwaldzki 2/4
50-384 Wrocław
POLAND

Contact:

Office: 10.3
Phone: +48 71 375 7093
E-mail: mirek[at]math.uni.wroc.pl

About me:

I am a member of the Institute for Advanced Study, Princeton, and an Assistant Professor in the
Department of Mathematics at Rutgers University and I am also a Professor in the Mathematical
Institute at the University of Wrocław. I was a member of the School of Mathematics at the Institute
for Advanced Study in Princeton. I completed my PhD in Mathematics at the University of Wrocław
in June 2011. I obtained my Habilitation degree from the University of Bonn in June 2016 and from
the University of Wrocław in June 2017.

The primary focus of my research to date has been understanding phenomena of norm and pointwise
convergence in analysis and ergodic theory that arise from dynamical systems as well as their interactions
with Fourier analysis, number theory, additive combinatorics and probability theory. Recently, I am also
interested in high-dimensional effects (dimension-free estimates) in analysis and convex geometry,
i.e. when the dimension tends to infinity.

My research is currently supported by the NSF grant DMS-2154712 (2022-2025).

Education and employment:


ETA($\eta$) Seminar:


I am running an online (ETA($\eta$)=) Ergodic Theory & Analysis Seminar. This is a seminar in ergodic theory and analysis
understood in a broad sense and their applications in additive combinatorics and additive number theory. The ETA($\eta$)
seminar is aimed at a general mathematical audience. Graduate and postdoctoral students are especially welcome
to attend. We meet over Zoom every Wednesday at 11am Eastern Time (New York).

Papers and preprints:

  1. J. Bourgain, M. Mirek, E.M. Stein, J. Wright. On a multi-parameter variant of the Bellow-Furstenberg problem.
    Submitted.

  2. M. Mirek, T. Z. Szarek, J. Wright. Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspective.
    To appear in the Revista Matemática Iberoamericana.

  3. A. D. Ionescu, Á. Magyar, M. Mirek, T. Z. Szarek. Polynomial averages and pointwise ergodic theorems on nilpotent groups.
    To appear in the Inventiones Mathematicae.

  4. M. Mirek, W. Słomian, T. Z. Szarek. Some remarks on oscillation inequalities.
    To appear in the Ergodic Theory & Dynamical Systems.

  5. A. Iosevich, B. Langowski, M. Mirek, T. Z. Szarek. Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres.
    Submitted.

  6. M. Mirek, T. Z. Szarek, B. Wróbel. Dimension-free estimates for the discrete spherical maximal functions.
    Submitted.

  7. B. Krause, M. Mirek, T. Tao. Pointwise ergodic theorems for non-conventional bilinear polynomial averages.
    Annals of Mathematics 195 (2022), no. 3, pp. 997-1109.

  8. D. Kosz, M. Mirek, P. Plewa, B. Wróbel. Some remarks on dimension-free estimates for the discrete Hardy-Littlewood maximal functions.
    Accepted for publication in the Israel Journal of Mathematics.

  9. C. Fefferman, A. Ionescu, T. Tao, S. Wainger; with contributions from
    L. Lanzani, A. Magyar, M. Mirek, A. Nagel, D. H. Phong, L. Pierce, F. Ricci, C. Sogge, B. Street.
    Analysis and applications: The mathematical work of Elias Stein.
    Bulletin of the American Mathematical Society 57 (2020), pp. 523-594.

  10. J. Bourgain, M. Mirek, E.M. Stein, B. Wróbel. On the Hardy-Littlewood maximal functions in high dimensions: Continuous and discrete perspective.
    P. Ciatti, A. Martini (eds.), Geometric Aspects of Harmonic Analysis. A conference proceedings on the occasion of Fulvio Ricci's 70th birthday Cortona, Italy, 25-29.06.2018.
    Springer INdAM Series 45, (2021), pp. 456.

  11. J. Bourgain, M. Mirek, E.M. Stein, B. Wróbel. On discrete Hardy-Littlewood maximal functions over the balls in $\mathbb Z^d$: dimension-free estimates.
    B. Klartag, E. Milman (eds.), Geometric Aspects of Functional Analysis, Israel Seminar (GAFA) 2017-2019,
    Volume I, Lecture Notes in Mathematics 2256, Chapter 8, 127-169.

  12. M. Mirek, E. M. Stein, P. Zorin-Kranich. Jump inequalities for translation-invariant polynomial averages and singular integrals on $\mathbb Z^d$.
    Advances in Mathematics 365 (2020), 107065, pp. 57.

  13. M. Mirek, E. M. Stein, P. Zorin-Kranich. A bootstrapping approach to jump inequalities and their applications.
    Analysis & PDE 13, (2020), no. 2, 527-558.

  14. M. Mirek, E. M. Stein, P. Zorin-Kranich. Jump inequalities via real interpolation.
    Mathematische Annalen 376, (2020), no. 1-2, 797-819.

  15. J. Bourgain, M. Mirek, E.M. Stein, B. Wróbel. Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in $\mathbb Z^d$.
    American Journal of Mathematics 141, (2019), no. 4, 857-905.

  16. M. Mirek, E. M. Stein, B. Trojan. $\ell^p(\mathbb Z^d)$-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates.
    Journal of Functional Analysis 277, (2019), no. 8, 2471-2521.

  17. J. Bourgain, M. Mirek, E.M. Stein, B. Wróbel. On dimension-free variational inequalities for averaging operators in $\mathbb R^d$.
    Geometric And Functional Analysis (GAFA) 28, (2018), no. 1, 58-99.

  18. M. Mirek. Square function estimates for discrete Radon transforms.
    Analysis & PDE 11, (2018), no. 3, 583-608.

  19. B. Krause, M. Mirek, B. Trojan. Two-parameter version of Bourgain's inequality I: Rational frequencies.
    Advances in Mathematics 323, (2018), 720-744.

  20. M. Mirek, E. M. Stein, B. Trojan. $\ell^p(\mathbb Z^d)$-estimates for discrete operators of Radon type: Variational estimates.
    Inventiones Mathematicae 209, (2017), no. 3, 665-748.

  21. M. Mirek, B. Trojan, P. Zorin-Kranich. Variational estimates for averages and truncated singular integrals along the prime numbers.
    Transactions of the American Mathematical Society 369, (2017), no. 8, 5403-5423.

  22. M. Mirek, C. Thiele. A local $T(b)$ theorem for perfect Calderón-Zygmund operators.
    Proceedings of the London Mathematical Society 114, (2017), no. 3, 35-59.

  23. B. Krause, M. Mirek, B. Trojan. On the Hardy-Littlewood majorant problem for arithmetic sets.
    Journal of Functional Analysis 271, (2016), no. 1, 164-181.

  24. M. Mirek, B. Trojan. Discrete maximal functions in higher dimensions and applications to ergodic theory.
    American Journal of Mathematics 138, (2016), no. 6, 1495-1532.

  25. M. Mirek, B. Trojan. Cotlar's ergodic theorem along the prime numbers.
    Journal of Fourier Analysis and Applications 21, (2015), no. 4, 822-848.

  26. M. Mirek. Weak type $(1,1)$ inequalities for discrete rough maximal functions.
    Journal d'Analyse Mathematique 127, (2015), no. 1, 247-281.

  27. M. Mirek. Roth's Theorem in the Piatetski-Shapiro primes.
    Revista Matemática Iberoamericana 31, (2015), no. 2, 617-656.

  28. M. Mirek. $\ell^p(\mathbb Z)$-boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems.
    Mathematische Zeitschrift 279, (2015), no. 1-2, 27-59.

  29. M. Mirek. Discrete analogues in harmonic analysis: maximal functions and singular integral operators.
    Mathematisches Forschungsinstitut Oberwolfach: Real Analysis, Harmonic Analysis and Applications, 20-26 July 2014.
    DOI: 10.4171/OWR/2014/34, Rep. no. 34, (2014), 1893-1896.

  30. D. Buraczewski, E. Damek, S. Mentemeier, M. Mirek. Heavy tailed solutions of multivariate smoothing transforms.
    Stochastic Processes and their Applications 123, (2013), 1947-1986.

  31. M. Mirek. On fixed points of a generalized multidimensional affine recursion.
    Probability Theory and Related Fields (2013), 156, no. 3-4, 665-705.

  32. E. Damek, S. Mentemeier, M. Mirek, J. Zienkiewicz. Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices.
    Potential Analysis (2013), 38 no. 3, 683-697.

  33. D. Buraczewski, E. Damek, M. Mirek. Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems.
    Stochastic Processes and their Applications 122, (2012), 42-67.

  34. M. Mirek. Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps.
    Probability Theory and Related Fields 151, (2011), no. 3, 705-734.

  35. M. Mirek. Convergence to stable laws and a local limit theorem for stochastic recursions.
    Colloquium Mathematicum 118, (2010), 705-720.

Updated: September, 2022.