Damian Dąbrowski

Damian Dąbrowski

Assistant professor

IMPAN

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.

Together with Tomasz Adamowicz we are running the Seminar in Geometric Function and Mapping Theory. The broad theme is analysis with a geometric flavour, with emphasis on analysis in metric spaces, geometric measure theory, and geometric PDEs. If you’re planning to be in Warsaw and you’d like to give a talk, just send me an e-mail!

In years 2025-2030 I am supported by the ERC Starting Grant Quantitative projection problems in geometric measure theory, grant no. 101219218.

Funded by the European Union and the European Research Council
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

D. Dąbrowski, T. Orponen (2025). On the logarithmic equilibrium measure on curves. Preprint.

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D. Dąbrowski (2024). Favard length and quantitative rectifiability. Preprint.

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D. Dąbrowski, M. Goering, T. Orponen (2024). On the dimension of s-Nikodým sets. Preprint.

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Publications

D. Dąbrowski, M. Villa (2025). Analytic capacity and dimension of sets with plenty of big projections. Trans. Amer. Math. Soc. 378, no. 6, 3897–3950.

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D. Dąbrowski (2025). Quantitative Besicovitch projection theorem for irregular sets of directions. Proc. Lond. Math. Soc. 130, no. 3, e70037.

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D. Dąbrowski (2024). Visible parts and slices of Ahlfors regular sets. Discrete Anal. 2024:17, 31 pp.

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A. Chang, D. Dąbrowski, T. Orponen, M. Villa (2024). Structure of sets with nearly maximal Favard length. Anal. PDE 17, no. 4, 1473–1500.

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D. Dąbrowski, T. Orponen, H. Wang (2024). How much can heavy lines cover?. J. Lond. Math. Soc. 109, no. 5, e12910.

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D. Dąbrowski, X. Tolsa (2024). The measures with L2-bounded Riesz transform and the Painlevé problem. To appear in Mem. Amer. Math. Soc.

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J. Azzam, D. Dąbrowski (2023). An α-number characterization of Lp spaces on uniformly rectifiable sets. Publ. Mat. 67, no. 2, 819–850.

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D. Dąbrowski, M. Villa (2023). Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups. Math. Proc. Cambridge Philos. Soc. 175, no. 2, 445-458.

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D. Dąbrowski, T. Orponen, M. Villa (2022). Integrability of orthogonal projections, and applications to Furstenberg sets. Adv. Math. 407, 108567.

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

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

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D. Dąbrowski (2021). Sufficient condition for rectifiability involving Wasserstein distance W2. J. Geom. Anal. 31, 8539–8606.

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D. Dąbrowski (2020). Necessary condition for rectifiability involving Wasserstein distance W2. Int. Math. Res. Not. IMRN 2020, no. 22, 8936–8972.

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D. Dąbrowski (2019). Characterization of Sobolev-Slobodeckij spaces using curvature energies. Publ. Mat. 63, no. 2, 663–677.

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Recent & Upcoming Talks

Quantifying the Besicovitch projection theorem
The Besicovitch projection theorem, which is one of the cornerstones of geometric measure theory, states the following: a set E of …
02 Feb 2026 — 06 Feb 2026 Westlake University, Hangzhou
The geometry of singular integral operators
Singular integral operators are among the most classical objects of study in harmonic analysis, arising naturally in complex analysis …
03 Dec 2025 IMPAN
Slides
Equilibrium measures on curves
In this talk I will discuss one of the most classical objects of study in potential theory: equilibrium measures for the logarithmic …
24 Nov 2025 TU Wien
Slides
Equilibrium measures on curves
In this talk I will discuss one of the most classical objects of study in potential theory: equilibrium measures for the logarithmic …
18 Nov 2025 Université Paris-Saclay
Equilibrium measures on curves
In this talk I will discuss one of the most classical objects of study in potential theory: equilibrium measures for the logarithmic …
06 Nov 2025 IMPAN
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