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.

Here is my CV.

Interests
  • quantitative rectifiability
  • singular integral operators in non-doubling setting
  • behaviour of sets and measures under orthogonal projections
  • Furstenberg sets
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 (2023). Visible parts and slices of Ahlfors regular sets. Preprint.

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

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D. Dąbrowski, M. Villa (2022). Analytic capacity and dimension of sets with plenty of big projections. Preprint.

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D. Dąbrowski, X. Tolsa (2021). The measures with $L^2$-bounded Riesz transform satisfying a subcritical Wolff-type energy condition. Preprint.

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Publications

D. Dąbrowski, M. Villa (2023). Necessary condition for the $L^2$ boundedness of the Riesz transform on Heisenberg groups. Math. Proc. Cambridge Philos. Soc. (appeared online).

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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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A. Chang, D. Dąbrowski, T. Orponen, M. Villa (2022). Structure of sets with nearly maximal Favard length. To appear in Anal. PDE.

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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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J. Azzam, D. Dąbrowski (2020). An $\alpha$-number characterization of $L^{p}$ spaces on uniformly rectifiable sets. To appear in Publ. Mat.

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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

Quantifying Besicovitch projection theorem
Besicovitch projection theorem is one of the fundamental results of geometric measure theory, and it states that a set of finite length …
26 Jan 2023 16:00 University of Warwick
Slides
Vitushkin’s conjecture and sets with plenty of big projections
In this talk I will describe recent progress made on Vitushkin’s conjecture, an old problem lying at the intersection of geometric …
23 Jan 2023 14:00 University of Warwick
Slides
From orthogonal projections to Furstenberg sets
Given $0<s<1$ and $0<t<2$, we say that a planar set $F$ is an $(s,t)$-Furstenberg set if there exists a $t$-dimensional …
06 Sep 2022 15:00 Porquerolles
Slides
Vitushkin’s conjecture and sets with plenty of big projections
In this talk I am going to describe recent progress made on Vitushkin’s conjecture: if $E$ has plenty of big projections, then …
06 Jun 2022 15:00 Centre de Recerca Matemàtica (Barcelona)
Slides
Vitushkin’s conjecture and sets with plenty of big projections
In this talk I am going to describe recent progress made on Vitushkin’s conjecture: if $E$ has plenty of big projections, then …
02 Jun 2022 12:00 UPV/EHU (Bilbao)
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