We have showed that some set-theoretic assumptions imply that there is no translation invariant Borel hull operation on the family of Lebesgue null sets and on the family of meager sets (in Rn). We have also proved that if the meager ideal admits a monotone Borel hull operation, then there is also a monotone Borel hull operation on the σ–algebra of sets with the property of Baire. 
We have studied exceptional points of measurable subsets of the real line with respect to different differentiation bases. 
We have examined properties of differences of ﬁnite binary sequences with a ﬁxed number of ones, treated as binary numbers from Z(2m). We have used these results to study topological and measure properties of algebraic sums and differences of natural supports of Bernoulli-like measures. We have also presented some characterization of measures which are singular to the Haar measure and of measures absolutely continuous with respect to the Haar measure in Polish groups. -
We have described sets with the Steinhaus property and sets with the Smital property in topological groups. We have also discussed the Smital properties with respect to different ideals. 
The habilitation application was submitted. The basis of the application are papers -.
Tomasz Filipczak, Andrzej Rosłanowski, Saharon Shelah, On Borel Hull Operations, Real Anal. Exchange, 40 (2014-15), 129-140.
Małgorzata Filipczak, Tomasz Filipczak, Grażyna Horbaczewska, Władysław Wilczyński, Remarks on exceptional points and differentiation bases, Acta Math. Hungar. 148 (2016), 370-385.
Małgorzata Filipczak, Tomasz Filipczak, Some algebraic properties of finite binary sequences, Tatra Mt. Math. Publ., 65 (2016), 93-104.
Artur Bartoszewicz, Małgorzata Filipczak, Tomasz Filipczak, On supports of probability Bernoulli-like measures, J. Math. Anal. Appl. 462 (2018), 26-35.
Małgorzata Filipczak, Tomasz Filipczak, Rafał Knapik, Sets with Steinhaus and Smital properties, J. Math. Anal. Appl. 472 (2019), 1167-1174.