I am a postdoctoral researcher at the Department of Mathematics and Statistics at the University of Jyväskylä. I am mostly interested in geometric measure theory, as well as its applications to harmonic analysis and PDEs. I work in the Geometric Measure Theory group, led by Katrin Fässler and Tuomas Orponen.

In years 2022-2025 I am supported by the Academy of Finland postdoctoral grant *Quantitative rectifiability and harmonic measure beyond the Ahlfors-David-regular setting*, grant No. 347123.

I defended my PhD in February 2021 at the Universitat Autònoma de Barcelona, where I worked under supervision of Xavier Tolsa.

Interests

- quantitative rectifiability
- singular integral operators in non-doubling setting
- behaviour of sets and measures under orthogonal projections
- visibility problems

Education

PhD in Mathematics, 2021

Universitat Autònoma de Barcelona

MSc in Mathematics, 2017

University of Warsaw

BSc in in Mathematics, 2015

University of Warsaw

(2024).

On the dimension of $s$-Nikodým sets.
Preprint.

(2024).
(2024).
(2022).
Structure of sets with nearly maximal Favard length.
Anal. PDE 17, no. 4, 1473–1500.

(2024).
How much can heavy lines cover?.
J. Lond. Math. Soc. 109, no. 5, e12910.

(2024).
Visible parts and slices of Ahlfors regular sets.
To appear in Discrete Anal.

(2024).
An $\alpha$-number characterization of $L^{p}$ spaces on uniformly rectifiable sets.
Publ. Mat. 67, no. 2, 819–850.

(2023).
Necessary condition for the $L^2$ boundedness of the Riesz transform on Heisenberg groups.
Math. Proc. Cambridge Philos. Soc. 175, no. 2, 445-458.

(2023).
Integrability of orthogonal projections, and applications to Furstenberg sets.
Adv. Math. 407, 108567.

(2022).
Cones, rectifiability, and singular integral operators.
Rev. Mat. Iberoam. 38, no. 4, 1287–1334.

(2022).
Analytic capacity and dimension of sets with plenty of big projections.
To appear in Trans. Amer. Math. Soc.

(2022).
Two examples related to conical energies.
Ann. Fenn. Math. 47, no. 1, 261–281.

(2022).
Sufficient condition for rectifiability involving Wasserstein distance $W_2$.
J. Geom. Anal. 31, 8539–8606.

(2021).
Necessary condition for rectifiability involving Wasserstein distance $W_2$.
Int. Math. Res. Not. IMRN 2020, no. 22, 8936–8972.

(2020).
Characterization of Sobolev-Slobodeckij spaces using curvature energies.
Publ. Mat. 63, no. 2, 663–677.

(2019).
- damian.m.dabrowski [at] jyu.fi
- P.O. Box 35 (MaD), 40014 University of Jyväskylä, Finland
- Office: MaD 338.