## Contact

Universität WienInstitut für Mathematik

Kurt Gödel Research Center for Mathematical Logic

Kolingasse 14-16, office 07.54

1090 Vienna

Austria

ein damqazian sobotawsx@edcgmrfvail tgbyhncomujm

(change gaps to dots; yes, "ein" is a part of the address)

## Mathematical interests

**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.

## Ongoing research projects

- with P. Borodulin-Nadzieja, Measures in the random model.
- with J. Rondoš, Complemented subspaces of C(K)-spaces.
- with T. Żuchowski, Forcings related to ideals and submeasures.

## Publications

### Book

- with J. Kąkol, W. Kubiś, M. López-Pellicer, Descriptive Topology in Selected Topics of Functional Analysis, 2nd Edition - Updated and Expanded, series Developments in Mathematics, Springer, New York, 2024, pp. 830, in press.

### Preprints

- D. Sobota, L. Zdomskyy, Construction under Martin's axiom of a Boolean algebra with the Grothendieck property but without the Nikodym property, submitted (2023), arXiv.
- C. Bargetz, J. Kąkol, D. Sobota, Continuous operators from spaces of Lipschitz functions, submitted (2024), arXiv.
- G. Plebanek, J. Rondoš, D. Sobota, Complemented subspaces of Banach spaces C(K×L), in preparation.
- J. Rondoš, D. Sobota, Copies of separable spaces C(L) in general spaces C(K), in preparation.
- D. Sobota, Grothendieck C(K)-spaces of small density, in preparation.

### Published and accepted papers

- W. Marciszewski, D. Sobota, L. Zdomskyy, On sequences of finitely supported measures related to the Josefson--Nissenzweig theorem, Topol. Appl. (2023), Special Issue on the Occasion of TopoSym 2022, accepted, arXiv.
- C. Bargetz, J. Kąkol, D. Sobota, On complemented copies of the space c
_{0}in spaces C_{p}(X,E), Math. Nachr. 297 (2024), no. 2, 644-656, arXiv. - J. Kąkol, D. Sobota, L. Zdomskyy, Grothendieck C(K)-spaces and the Josefson--Nissenzweig theorem, Fund. Math. 263 (2023), no. 2, 105-131, arXiv.
- P. Borodulin-Nadzieja, D. Sobota, There is a P-measure in the random model, Fund. Math. 262 (2023), no. 3, 235-257, arXiv.
- W. Marciszewski, D. Sobota, The Josefson--Nissenzweig theorem and filters on ω, Arch. Math. Logic (2023), accepted, arXiv.
- D. Sobota, L. Zdomskyy, Convergence of measures after adding a real, Arch. Math. Logic 63 (2024), 135-162, arXiv.
- J. Kąkol, D. Sobota, L. Zdomskyy, On complementability of c
_{0}in spaces C(K×L), Proc. Amer. Math. Soc. (2022), accepted, arXiv. - D. Sobota, L. Zdomskyy, Minimally generated Boolean algebras with the Nikodym property, Topol. Appl. 323 (2023), Special Issue in Memory of Kenneth Kunen, 108298, arXiv.
- P. Borodulin-Nadzieja, D. Sobota, On sequences of homomorphisms into measure algebras and the Efimov problem, J. Symb. Logic 88 (2023), no. 1, 191-218, arXiv.
- D. Sobota, Convergence of measures on Boolean algebras and cardinal characteristics of the continuum, survey, RIMS Kôkyûroku 2164 (2020), 50-63, link.
- J. Kąkol, W. Marciszewski, D. Sobota, L. Zdomskyy, On complemented copies of the space c
_{0}in spaces C_{p}(X×Y), Israel J. Math. 250 (2022), 139-177, arXiv. - D. Sobota, L. Zdomskyy, Convergence of measures in forcing extensions, Israel J. Math. 232 (2019), no. 2, 501-529, arXiv.
- D. Sobota, L. Zdomskyy, The Nikodym property in the Sacks model, Topol. Appl. 230C (2017), 24-34, DOI, preprint.
- D. Sobota, On families of subsets of natural numbers deciding the norm convergence in ℓ
_{1}, Proc. Amer. Math. Soc. 146 (2018), no. 4, 1673-1680. - D. Sobota, Families of sets related to Rosenthal's lemma, Arch. Math. Logic 58 (2019), no. 1, 53-69, DOI, preprint.
- D. Sobota, The Nikodym property and cardinal characteristics of the continuum, Ann. Pure Appl. Logic 170 (2019), no. 1, 1-35, DOI, preprint.
- G. Plebanek, D. Sobota, Countable tightness in the spaces of regular probability measures, Fund. Math. 229:2 (2015), 159-169, DOI, arXiv.
- D. Sobota, Fibers of generic maps on surfaces, Topol. Appl. 161 (2014), 163-177, DOI, preprint.

## Awards

**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

**honors.**

*summa cum laude***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.

## Trivia

**My Erdös number is 3** through G. Plebanek → A. Blass → P. Erdös.

My brother **Daniel Sobota** is a philosopher.