Tomasz Z. Szarek

About me:

My mathematical interest focuses mainly on real and Fourier analysis and its applications to other fields of mathematics. During my Ph.D studies I was working mainly on problems related to the area called harmonic analysis of orthogonal expansions. Later on I got interested in spherical analysis. My most recent interests concern discrete harmonic analysis (both commutative and noncommutative) and its applications to ergodic theory. I was a member of Bilbao Analysis and PDE research group. 

E-mail:
szarektomaszz(at)gmail.com
tzszarek(at)uga.edu

Affiliation:
UGA - University of Georgia, Athens, GA 30605, USA

ETA Seminar:
I am co organizing Ergodic Theory & Analysis Seminar, which is an online seminar in ergodic theory and analysis understood in a broad sense.

Education and employment:

• 2023-: Assistant Professor, UGA - University of Georgia, USA

• 2023: Habilitation in Mathematics, University of Wrocław, Poland 

• 2020-2023: Postdoctoral, BCAM - Basque Center for Applied Mathematics, Spain

• 2018-2020: Postdoctoral, Rutgers University, USA

• 2018-: Assistant Professor, University of Wrocław, Poland (on leave)

• 2017/18: Postdoctoral, Institute of Mathematics of the Polish Academy of Sciences, Poland

• 2016/17: Postdoctoral, University of Warsaw, Poland

• 2015/16: Postdoctoral, Institute of Mathematics of the Polish Academy of Sciences, Poland

• 2015: PhD degree in Mathematics, Institute of Mathematics of the Polish Academy of Sciences, Poland 

• 2011: M.Sc. in Mathematics, Wrocław University of Technology, Poland

Preprints:

22. A. Nowak, P. Sjögren, T.Z. Szarek,
New sharp bounds for the Jacobi heat kernel via an extension of the Dijksma-Koornwinder formula,
preprint 2024. arXiv:2402.08800

Published papers:

21. A.D. Ionescu, Á. Magyar, M. Mirek, T.Z. Szarek,
Polynomial sequences in discrete nilpotent groups of step 2,
Adv. Nonlinear Stud. 23 (2023), no. 1, ans-2023-0085. arXiv:2212.14136 

20. A. Nowak, L. Roncal, T.Z. Szarek,
Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions,
Commun. Pure Appl. Anal. 22 (2023), 2233-2277. arXiv:2201.00327

19. A. Iosevich, B. Langowski, M. Mirek, T.Z. Szarek,
Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres,
Math. Ann. 388 (2024), 2041-2120. arXiv:2106.12015

18. M. Mirek, T.Z. Szarek, B. Wróbel,
Dimension-free estimates for the discrete spherical maximal functions,
Int. Math. Res. Not. IMRN 2024 (2024), 901-963. arXiv:2012.14509

17. A.D. Ionescu, Á. Magyar, M. Mirek, T.Z. Szarek,
Polynomial averages and pointwise ergodic theorems on nilpotent groups,
Invent. Math. 231 (2023), 1023-1140. arXiv:2112.03322

16. M. Mirek, W. Słomian, T.Z. Szarek,
Some remarks on oscillation inequalities,
Ergodic Theory Dynam. Systems 43 (2023), 3383-3412. arXiv:2110.01149

15. M. Mirek, T.Z. Szarek, J. Wright,
Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives,
Rev. Mat. Iberoam. 38 (2022), 2249-2284. arXiv:2209.01309

14. A. Nowak, P. Sjögren, T.Z. Szarek,
Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces, for Jacobi expansions, on a ball and on a simplex,
Math. Ann. 381 (2021), 1455-1476. arXiv:1905.10581

13. A. Nowak, P. Sjögren, T.Z. Szarek,
Sharp estimates of the spherical heat kernel,
J. Math. Pures Appl. 129 (2019), 23-33. arXiv:1802.09385 

12. P. Sjögren, T.Z. Szarek,
Analysis in the multi-dimensional ball,
Mathematika 65 (2019), 190-212. arXiv:1803.06195 

11. T.Z. Szarek,
Lusin area integrals related to Jacobi expansions,
Monatsh. Math. 189 (2019), 157-178. arXiv:1701.02289 

10. A. Nowak, P. Sjögren, T.Z. Szarek,
Maximal operators of exotic and non-exotic Laguerre and other semigroups associated with classical orthogonal expansions,
Adv. Math. 318 (2017), 307-354. arXiv:1607.00979 

9. A. Nowak, K. Stempak, T.Z. Szarek,
On harmonic analysis operators in Laguerre-Dunkl and Laguerre symmetrized settings,
SIGMA 12 (2016), 096, 39 pages. arXiv:1602.05369

8. A.J. Castro, A. Nowak, T.Z. Szarek,
Riesz-Jacobi transforms as principal value integrals,
J. Fourier Anal. Appl. 22 (2016), 493-541. arXiv:1405.7069

7. A. Nowak, P. Sjögren, T.Z. Szarek,
Analysis related to all admissible type parameters in the Jacobi setting,
Constr. Approx. 41 (2015), 185-218. arXiv:1211.3270

6. A.J. Castro, T.Z. Szarek,
On fundamental harmonic analysis operators in certain Dunkl and Bessel settings,
J. Math. Anal. Appl. 412 (2014), 943-963. arXiv:1304.2904  

5. A.J. Castro, T.Z. Szarek,
Calderón-Zygmund operators in the Bessel setting for all possible type indices,
Acta Math. Sin. (Engl. Ser.) 30 (2014), 637-648. arXiv:1110.5659 

4. T.Z. Szarek,
On Lusin's area integrals and g-functions in certain Dunkl and Laguerre settings,
Math. Nachr. 285 (2012), 1517-1542. arXiv:1011.0898 

3. T.Z. Szarek,
Multipliers of Laplace transform type in certain Dunkl and Laguerre settings,
Bull. Aust. Math. Soc. 85 (2012), 177-190. arXiv:1101.4139  

2. A. Nowak, T.Z. Szarek,
Calderón-Zygmund operators related to Laguerre function expansions of convolution type,
J. Math. Anal. Appl. 388 (2012), 801-816. arXiv:1102.1633 

1. T.Z. Szarek,
Littlewood-Paley-Stein type square functions based on Laguerre semigroups,
Acta Math. Hungar. 131 (2011), 59-109. arXiv:1001.3579