Damian Sobota

Damian Sobota, PhD

Contact

Universität Wien
Institut 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

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

Publications

Book

  1. 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

  1. 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.
  2. C. Bargetz, J. Kąkol, D. Sobota, Continuous operators from spaces of Lipschitz functions, submitted (2024), arXiv.
  3. G. Plebanek, J. Rondoš, D. Sobota, Complemented subspaces of Banach spaces C(K×L), submitted (2024), arXiv.
  4. J. Rondoš, D. Sobota, Copies of separable spaces C(L) in general spaces C(K), in preparation.
  5. D. Sobota, Grothendieck C(K)-spaces of small density, in preparation.

Published and accepted papers

  1. 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.
  2. C. Bargetz, J. Kąkol, D. Sobota, On complemented copies of the space c0 in spaces Cp(X,E), Math. Nachr. 297 (2024), no. 2, 644-656, arXiv.
  3. J. Kąkol, D. Sobota, L. Zdomskyy, Grothendieck C(K)-spaces and the Josefson--Nissenzweig theorem, Fund. Math. 263 (2023), no. 2, 105-131, arXiv.
  4. P. Borodulin-Nadzieja, D. Sobota, There is a P-measure in the random model, Fund. Math. 262 (2023), no. 3, 235-257, arXiv.
  5. W. Marciszewski, D. Sobota, The Josefson--Nissenzweig theorem and filters on ω, Arch. Math. Logic (2023), accepted, arXiv.
  6. D. Sobota, L. Zdomskyy, Convergence of measures after adding a real, Arch. Math. Logic 63 (2024), 135-162, arXiv.
  7. J. Kąkol, D. Sobota, L. Zdomskyy, On complementability of c0 in spaces C(K×L), Proc. Amer. Math. Soc. (2022), accepted, arXiv.
  8. 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.
  9. 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.
  10. D. Sobota, Convergence of measures on Boolean algebras and cardinal characteristics of the continuum, survey, RIMS Kôkyûroku 2164 (2020), 50-63, link.
  11. J. Kąkol, W. Marciszewski, D. Sobota, L. Zdomskyy, On complemented copies of the space c0 in spaces Cp(X×Y), Israel J. Math. 250 (2022), 139-177, arXiv.
  12. D. Sobota, L. Zdomskyy, Convergence of measures in forcing extensions, Israel J. Math. 232 (2019), no. 2, 501-529, arXiv.
  13. D. Sobota, L. Zdomskyy, The Nikodym property in the Sacks model, Topol. Appl. 230C (2017), 24-34, DOI, preprint.
  14. D. Sobota, On families of subsets of natural numbers deciding the norm convergence in ℓ1, Proc. Amer. Math. Soc. 146 (2018), no. 4, 1673-1680.
  15. D. Sobota, Families of sets related to Rosenthal's lemma, Arch. Math. Logic 58 (2019), no. 1, 53-69, DOI, preprint.
  16. D. Sobota, The Nikodym property and cardinal characteristics of the continuum, Ann. Pure Appl. Logic 170 (2019), no. 1, 1-35, DOI, preprint.
  17. G. Plebanek, D. Sobota, Countable tightness in the spaces of regular probability measures, Fund. Math. 229:2 (2015), 159-169, DOI, arXiv.
  18. 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 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.

Trivia

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

My brother Daniel Sobota is a philosopher.