University of Wrocław

Mathematical Institute

Plac Grunwaldzki 2/4

50-384 Wrocław

POLAND

Office: 10.3

Phone: +48 71 375 7093

E-mail: mirek[at]math.uni.wroc.pl

I am a member of the School of Mathematics at the Institute for Advanced Study in Princeton

and I am an associate professor in the Mathematical Institute at the University of Wrocław.

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 University of Wrocław

in June 2017. My research interests are concentrated in the field of harmonic analysis and its

applications to ergodic theory and probability theory.

- Member of the Institute for Advanced Study, Princeton, (09.2016-08.2017).
- Habilitation in Mathematics at the University of Wrocław, (20.06.2017).
- Habilitation in Mathematics at the University of Bonn, (08.06.2016).
- HCM Postdoctoral research fellowship at the University of Bonn, (10.2012-08.2016).
- Assistant professor in the Mathematical Institute of University of Wrocław, (10.2011-09.2018). On leave.
- PhD in Mathematics from the University of Wrocław, (07.06.2011).
- M.Sc. in Mathematics from the University of Wrocław, (05.09.2007).

Wybrane zagadnienia z analizy harmonicznej.

- J. Bourgain, M. Mirek, E.M. Stein and B. Wróbel.
On dimension-free variational inequalities for averaging operators in $\mathbb R^d$.

Submitted.

- M. Mirek, E. M. Stein and B. Trojan.
$\ell^p(\mathbb Z^d)$-estimates for discrete operators of Radon type:
Maximal functions and vector-valued estimates.

Submitted.

- B. Krause, M. Mirek and B. Trojan.
Two-parameter version
of Bourgain's inequality I: Rational frequencies.

Accepted for publication in the Advances in Mathematics.

- M. Mirek.
Square function estimates for discrete Radon transforms.

Accepted for publication in the Analysis & PDE.

- M. Mirek, E. M. Stein and B. Trojan.
$\ell^p(\mathbb Z^d)$-estimates for discrete operators of Radon type:
Variational estimates.

Inventiones Mathematicae**209**, (2017), no. 3, 665-748.

- M. Mirek, B. Trojan and 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.

- M. Mirek and C. Thiele.
A local $T(b)$ theorem for
perfect Calderón-Zygmund operators.

Proceedings of the London Mathematical Society**114**, (2017), no. 3, 35-59.

- B. Krause, M. Mirek and B. Trojan.
On the
Hardy-Littlewood majorant problem for arithmetic sets.

Journal of Functional Analysis**271**, (2016), no. 1, 164-181.

- M. Mirek and B. Trojan.
Discrete maximal functions in
higher dimensions and applications to ergodic theory.

American Journal of Mathematics**138**, (2016), no. 6, 1495-1532.

- M. Mirek and B. Trojan.
Cotlar's ergodic theorem along the prime numbers.

Journal of Fourier Analysis and Applications**21**, (2015), no. 4, 822-848.

- M. Mirek.
Weak type $(1,1)$ inequalities for discrete rough maximal
functions.

Journal d'Analyse Mathematique**127**, (2015), no. 1, 247-281.

- M. Mirek.
Roth's Theorem in the Piatetski-Shapiro primes.

Revista Matemática Iberoamericana**31**, (2015), no. 2, 617-656.

- 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.

- 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.

- D. Buraczewski, E. Damek, S. Mentemeier and M. Mirek.
Heavy tailed solutions of multivariate smoothing transforms.

Stochastic Processes and their Applications**123**, (2013), 1947-1986.

- M. Mirek.
On fixed points of a
generalized multidimensional affine recursion.

Probability Theory and Related Fields (2013),**156**, no. 3-4, 665-705.

- E. Damek, S. Mentemeier, M. Mirek and J. Zienkiewicz.
Convergence to stable laws for
multidimensional stochastic recursions: the case
of regular matrices.

Potential Analysis (2013),**38**no. 3, 683-697.

- D. Buraczewski, E. Damek and 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.

- 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.

- M. Mirek.
Convergence to
stable laws and a local limit theorem for stochastic
recursions.

Colloquium Mathematicum**118**, (2010), 705-720.

Updated: 20.09.2017