Damian Dąbrowski

Damian Dąbrowski

Postdoc in mathematics

University of Jyväskylä

About me

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

Preprints

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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D. Dąbrowski, X. Tolsa (2024). The measures with $L^2$-bounded Riesz transform and the Painlevé problem. Preprint.

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D. Dąbrowski (2022). Quantitative Besicovitch projection theorem for irregular sets of directions. Preprint.

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Publications

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

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J. Azzam, D. Dąbrowski (2023). An $\alpha$-number characterization of $L^{p}$ 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 $L^2$ 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, M. Villa (2022). Analytic capacity and dimension of sets with plenty of big projections. To appear in Trans. Amer. Math. Soc.

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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 $W_2$. J. Geom. Anal. 31, 8539–8606.

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D. Dąbrowski (2020). Necessary condition for rectifiability involving Wasserstein distance $W_2$. 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

Favard length and quantitative rectifiability
Favard length of a planar set is the average length of its orthogonal projections. The Besicovitch projection theorem, which is one of …
11 Dec 2024 University of Jyväskylä
Favard length and quantitative rectifiability
Favard length of a planar set is the average length of its orthogonal projections. The Besicovitch projection theorem, which is one of …
14 Nov 2024 Universidad Complutense Madrid
Favard length and quantitative rectifiability
Favard length of a planar set is the average length of its orthogonal projections. The Besicovitch projection theorem, which is one of …
07 Nov 2024 Universitat Autònoma de Barcelona
Favard length and quantitative rectifiability
Favard length of a set is the average length of its orthogonal projections. The Besicovitch projection theorem states the following: …
10 Sep 2024 IMPAN (Warsaw)
Slides
Favard length problem for Ahlfors regular sets
Favard length of a set is the average length of its orthogonal projections. The Besicovitch projection theorem states the following: …
25 Jul 2024 University of Washington
Slides
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