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 and Harmonic Analysis group, led by Tuomas Orponen and Katrin Fässler.

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

Cite arXiv

A. Chang, D. Dąbrowski, T. Orponen, M. Villa (2022). Structure of sets with nearly maximal Favard length. Preprint.

Cite arXiv

D. Dąbrowski, T. Orponen, M. Villa (2021). Integrability of orthogonal projections, and applications to Furstenberg sets. Preprint.

Cite arXiv

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

Cite arXiv

D. Dąbrowski, M. Villa (2020). Necessary condition for the $L^2$ boundedness of the Riesz transform on Heisenberg groups. Preprint.

Cite arXiv

Publications

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

Cite Article arXiv

D. Dąbrowski (2021). Cones, rectifiability, and singular integral operators. Appeared online in Rev. Mat. Iberoam.

Cite Article arXiv

D. Dąbrowski (2021). Sufficient condition for rectifiability involving Wasserstein distance $W_2$. J. Geom. Anal. 31, 8539–8606.

Cite Article ReadCube arXiv

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

Cite arXiv

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

Cite Article arXiv

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

Cite Article arXiv

Recent & Upcoming Talks

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)
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 Basque Center for Applied Mathematics (Bilbao)
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 Feb 2022 15:30 Hausdorff Research Institute for Mathematics
Video
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 …
05 Jan 2022 10:30 Tampere University
On measures with $L^2$ bounded Riesz transform: to AD regularity and beyond!
The measures which define an $L^2$ bounded $n$-dimensional Riesz transform have been intensely studied in the last 50 years. Especially …
28 Oct 2021 10:30 Aalto University
See all events

Contact