Mariusz Mirek
Rutgers University
Department of Mathematics
Hill Center-Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019
USA
Contact:
Office: Hill Center 542
Phone: 848-445-6753
E-mail: mariusz.mirek[at]rutgers.edu
About me:
I am an Assistant Professor in the Department of Mathematics at
Rutgers University and
I am an Associate 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 ergodic theory that
arise from dynamical systems consideratins as well as
their interactions with
Fourier analysis, number theory, additive combinatorics and
probability theory.
Education and employment:
- Assistant Professor in the Department of Mathematics at Rutgers University, (09.2018-Now).
- Lecturer in the Department of Mathematics at King's College London, (05.2017-09.2017).
- Member of the Institute for Advanced Study, Princeton, (09.2016-08.2017).
- Habilitation in Mathematics from the University of Wrocław, (20.06.2017).
- Habilitation in Mathematics from the University of Bonn, (08.06.2016).
- Associate Professor in the Mathematical Institute at the University of Wrocław, (10.2014-On leave).
- HCM Postdoctoral Research Fellowship at the University of Bonn, (10.2012-08.2016).
- Assistant Professor in the Mathematical Institute at the University of Wrocław, (10.2011-09.2014).
- PhD in Mathematics from the University of Wrocław, (07.06.2011).
- M.Sc. in Mathematics from the University of Wrocław, (05.09.2007).
Papers and preprints:
- B. Krause, M. Mirek and T. Tao.
Pointwise ergodic theorems for non-conventional bilinear polynomial averages.
-
C. Fefferman, A. Ionescu, T. Tao and 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.
- J. Bourgain, M. Mirek, E.M. Stein and B. Wróbel.
On the Hardy--Littlewood
maximal functions in high dimensions: Continuous and discrete
perspective.
- M. Mirek, E. M. Stein, P. Zorin-Kranich.
Jump inequalities for
translation-invariant polynomial averages and singular integrals on
$\mathbb Z^d$.
- J. Bourgain, M. Mirek, E.M. Stein and B. Wróbel.
On discrete
Hardy--Littlewood maximal functions over the balls in $\mathbb Z^d$:
dimension-free estimates.
- M. Mirek, E. M. Stein, P. Zorin-Kranich.
A bootstrapping approach
to jump inequalities and their applications.
- M. Mirek, E. M. Stein, P. Zorin-Kranich.
Jump inequalities via real
interpolation.
- J. Bourgain, M. Mirek, E.M. Stein and B. Wróbel.
Dimension-free estimates
for discrete Hardy-Littlewood averaging operators over the
cubes in $\mathbb Z^d$.
- 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.
- J. Bourgain, M. Mirek, E.M. Stein and B. Wróbel.
On dimension-free
variational inequalities for averaging operators in $\mathbb R^d$.
- M. Mirek.
Square function estimates
for discrete Radon transforms.
- B. Krause, M. Mirek and B. Trojan.
Two-parameter version of
Bourgain's inequality I: Rational frequencies.
- M. Mirek, E. M. Stein and B. Trojan.
$\ell^p(\mathbb Z^d)$-estimates
for discrete operators of Radon type: Variational estimates.
- M. Mirek, B. Trojan and P. Zorin-Kranich.
Variational estimates for
averages and truncated singular integrals along the prime numbers.
- M. Mirek and C. Thiele.
A local $T(b)$ theorem for
perfect Calderón-Zygmund operators.
- B. Krause, M. Mirek and B. Trojan.
On the Hardy-Littlewood
majorant problem for arithmetic sets.
- M. Mirek and B. Trojan.
Discrete maximal functions
in higher dimensions and applications to ergodic theory.
- M. Mirek and B. Trojan.
Cotlar's ergodic theorem
along the prime numbers.
- M. Mirek.
Weak type $(1,1)$
inequalities for discrete rough maximal functions.
- M. Mirek.
Roth's Theorem in the
Piatetski-Shapiro primes.
- M. Mirek.
$\ell^p(\mathbb Z)$-boundedness
of discrete maximal functions along thin subsets of primes and
pointwise ergodic theorems.
- M. Mirek.
Discrete
analogues in harmonic analysis: maximal functions and singular
integral operators.
- D. Buraczewski, E. Damek, S. Mentemeier and M. Mirek.
Heavy tailed solutions of
multivariate smoothing transforms.
- M. Mirek.
On fixed points of a
generalized multidimensional affine recursion.
- E. Damek, S. Mentemeier, M. Mirek and J. Zienkiewicz.
Convergence to stable laws
for multidimensional stochastic recursions: the case of regular
matrices.
- D. Buraczewski, E. Damek and M. Mirek.
Asymptotics of stationary
solutions of multivariate stochastic recursions with heavy tailed
inputs and related limit theorems.
- M. Mirek.
Heavy tail phenomenon and
convergence to stable laws for iterated Lipschitz maps.
- M. Mirek.
Convergence
to stable laws and a local limit theorem for stochastic
recursions.
Updated: August 05, 2020.