Institut für Mathematik
Kurt Gödel Research Center for Mathematical Logic
Kolingasse 14-16, office 07.54
ein damqazian sobotawsx@edcgmrfvail tgbyhncomujm
(change gaps to dots; yes, "ein" is a part of the address)
Applications of infinitary combinatorics and forcing to measure theory and Banach space theory.
My PhD advisor at the Institute of Mathematics of Polish Academy of Sciences was Prof. Piotr Koszmider.
Organizing activitiesI am an organizer of the session Functional Analysis in Topology of the 36th Summer Topology Conference held from 18th to 22nd July 2022 in Vienna.
Publications and ongoing projects
- with C. Bargetz and J. Kąkol, Topological aspects of Lipschitz spaces.
- with P. Borodulin-Nadzieja, Measures in the random model.
- Grothendieck C(K)-spaces of small density.
Published or submitted papers
- with P. Borodulin-Nadzieja, There is a P-measure in the random model, 2022, preprint, submitted.
- with W. Marciszewski, The Josefson-Nissenzweig theorem and filters on ω, 2022, preprint, submitted.
- with L. Zdomskyy, Convergence of measures after adding a real, 2021, preprint, submitted.
- with C. Bargetz and J. Kąkol, On complemented copies of the space c0 in spaces Cp(X,E), 2021, preprint, submitted.
- with L. Zdomskyy, Minimally generated Boolean algebras with the Nikodym property, Topol. Appl. 2021, accepted.
- with P. Borodulin-Nadzieja, On sequences of homomorphisms into measure algebras and the Efimov problem, J. Symb. Logic (2021), accepted.
- Convergence of measures on Boolean algebras and cardinal characteristics of the continuum, survey, RIMS Kôkyûroku 2164 (2020), 50-63, link.
- with J. Kąkol, W. Marciszewski, L. Zdomskyy, On complemented copies of the space c0 in spaces Cp(X×Y), Israel J. Math. (2021), accepted.
- with J. Kąkol, L. Zdomskyy, On complementability of c0 in spaces C(K×L), 2022, preprint, submitted.
- with J. Kąkol, L. Zdomskyy, The Josefson-Nissenzweig theorem, Grothendieck property, and finitely supported measures on compact spaces, 2020, preprint, submitted.
- with L. Zdomskyy, Convergence of measures in forcing extensions, Israel J. Math. 232 (2019), no. 2, 501-529, preprint.
- with L. Zdomskyy, The Nikodym property in the Sacks model, Topol. Appl. 230C (2017), 24-34, DOI, preprint.
- On families of subsets of natural numbers deciding the norm convergence in ℓ1, Proc. Amer. Math. Soc. 146 (2018), no. 4, 1673-1680, DOI, preprint.
- Families of sets related to Rosenthal's lemma, Arch. Math. Logic 58 (2019), no. 1, 53-69, DOI, preprint.
- The Nikodym property and cardinal characteristics of the continuum, Ann. Pure Appl. Logic 170 (2019), no. 1, 1-35, DOI, preprint.
- with G. Plebanek, Countable tightness in the spaces of regular probability measures, Fund. Math. 229:2 (2015), 159-169, DOI, arXiv.
- Fibers of generic maps on surfaces, Topol. Appl. 161 (2014), 163-177, DOI, preprint.
Wacław Marszałek Award, 1st Degree Award of the Director of the Institute of Mathematics of Polish Academy of Sciences for the Distinguished PhD Thesis, 2017.
My PhD thesis Cardinal invariants of the continuum and convergence of measures on compact spaces was awarded summa cum laude honors.
Second Prize in the Józef Marcinkiewicz Contest for the Best Student Paper in Mathematics organized by the Polish Mathematical Society (56th edition, 2012).
Scholarship for the Best PhD students, Institute of Mathematics, Polish Academy of Sciences, 2014-2015.
Polish Minister of Science and Higher Education Scholarship for Outstanding Results in Study, twice: 2009-2010 and 2010-2011.
My Erdös number is 3 through G. Plebanek → A. Blass → P. Erdös.
My brother Daniel Sobota is a philosopher.