About me

I am a postdoc 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 group of 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.

Research

Papers

  1. Two examples related to conical energies. 
    Preprint (2020). arXiv:2011.12717
  2. An α-number characterization of Lp spaces on uniformly rectifiable sets (with J. Azzam).
    Preprint (2020). arXiv:2009.10111
  3. Cones, rectifiability, and singular integral operators.
    Preprint (2020). arXiv:2006.14432
  4. Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups (with M. Villa).
    Preprint (2020). arXiv:2004.01117
  5. Necessary condition for rectifiability involving Wasserstein distance W2.
    Int. Math. Res. Not. IMRN 2020 (2020), no. 22, 8936–8972.
  6. Sufficient condition for rectifiability involving Wasserstein distance W2.
    J. Geom. Anal. (2021). ReadCube.
  7. Characterization of Sobolev-Slobodeckij spaces using curvature energies.
    Publ. Mat. 63 (2019), 663–677.

Slides

  1. Cones, rectifiability and singular integral operators; slides, video – Analysis and PDE Working Summer Seminar, University of Minnesota, June 2020
  2. Cones, rectifiability and singular integral operators – Edinburgh, April 2020
  3. Cones and rectifiability – Warsaw, October 2019
  4. Rectifiability of measures via optimal transport – Barcelona,  June 2019
  5. Rectifiability of measures via optimal transport – Helsinki,  June 2019
  6. Rectifiability of measures via optimal transport – Toulouse, February 2019
  7. Rectifiability of measures via optimal transport – Barcelona, January 2019

PhD thesis

Rectifiability of Radon measures – thesis, slides.

Contact

ORCID iD icon orcid.org/0000-0003-4495-6090

E-mail: ddabrowski [at] mat.uab.cat

Mailing address:
Departament de Matemàtiques, Universitat Autònoma de Barcelona,
Edifici C Facultat de Ciències,
08193 Bellaterra (Barcelona), Spain

Office: C1/-166

About my surname: If you are wondering how to pronounce “Dąbrowski”, phonetically it is “dɔmˈbrɔfskʲi“, and an English approximation would be “Dombrofsky” or “Dombrosky”.
To write “Dąbrowski” in LaTeX, try “D{\k{a}}browski”.
Fun fact: the surname appears several times in the Polish national anthem.