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

Publications

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

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(2023). An $\alpha$-number characterization of $L^{p}$ spaces on uniformly rectifiable sets. Publ. Mat. 67, no. 2, 819–850.

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(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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(2022). Integrability of orthogonal projections, and applications to Furstenberg sets. Adv. Math. 407, 108567.

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

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(2022). Structure of sets with nearly maximal Favard length. To appear in Anal. PDE.

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

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

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

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