About me
I am an assistant professor at the Institute of Mathematics of the Polish Academy of Sciences (IMPAN). I am mostly interested in geometric measure theory, as well as its applications to harmonic analysis and PDEs.
In years 2025-2030 I am supported by the ERC Starting Grant Quantitative projection problems in geometric measure theory, grant no. 101219218.
Interests
- quantitative rectifiability
- singular integral operators in non-doubling setting
- behaviour of sets and measures under orthogonal projections
- visibility problems
- potential theory
Education
PhD in Mathematics, 2021
Universitat Autònoma de Barcelona
MSc in Mathematics, 2017
University of Warsaw
BSc in in Mathematics, 2015
University of Warsaw
Preprints
(2025).
On the logarithmic equilibrium measure on curves.
Preprint.
(2024).
Favard length and quantitative rectifiability.
Preprint.
(2024).
On the dimension of
Publications
(2025).
Analytic capacity and dimension of sets with plenty of big projections.
Trans. Amer. Math. Soc. 378, no. 6, 3897–3950.
(2025).
Quantitative Besicovitch projection theorem for irregular sets of directions.
Proc. Lond. Math. Soc. 130, no. 3, e70037.
(2024).
Visible parts and slices of Ahlfors regular sets.
Discrete Anal. 2024:17, 31 pp.
(2024).
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).
The measures with
(2023).
An
(2023).
Necessary condition for the
(2022).
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).
Two examples related to conical energies.
Ann. Fenn. Math. 47, no. 1, 261–281.
(2021).
Sufficient condition for rectifiability involving Wasserstein distance
(2020).
Necessary condition for rectifiability involving Wasserstein distance
(2019).
Characterization of Sobolev-Slobodeckij spaces using curvature energies.
Publ. Mat. 63, no. 2, 663–677.
Recent & Upcoming Talks
Contact
- damian.m.dabrowski [at] jyu.fi
- P.O. Box 35 (MaD), 40014 University of Jyväskylä, Finland
- Office: MaD 338.