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
Publications
(2021).
The measures with $L^2$-bounded Riesz transform satisfying a subcritical Wolff-type energy condition.
Preprint.
(2021).
Sufficient condition for rectifiability involving Wasserstein distance $W_2$.
J. Geom. Anal. 31, 8539–8606.
(2020).
Two examples related to conical energies.
To appear in Ann. Acad. Sci. Fenn. Math.
(2020).
An $\alpha$-number characterization of $L^{p}$ spaces on uniformly rectifiable sets.
Preprint.
(2020).
Cones, rectifiability, and singular integral operators.
To appear in Rev. Mat. Iberoam.
(2020).
Necessary condition for rectifiability involving Wasserstein distance $W_2$.
Int. Math. Res. Not. IMRN 2020, no. 22, 8936–8972.
(2020).
Necessary condition for the $L^2$ boundedness of the Riesz transform on Heisenberg groups.
Preprint.
(2019).
Characterization of Sobolev-Slobodeckij spaces using curvature energies.
Publ. Mat. 63, no. 2, 663–677.
Recent & Upcoming Talks
Contact
- damian.m.dabrowski [at] jyu.fi
- P.O. Box 35 (MaD), 40014 University of Jyväskylä, Finland
- Office: MaD 338.