Damian Sobota

Damian Sobota, PhD

Contact

Universität Wien
Institut für Mathematik
Kurt Gödel Research Center for Mathematical Logic
Augasse 2-6, office C5.26.4
1090 Vienna
Austria
ein  damqazian  sobotawsx@edcgmrfvail  tgbyhncomujm
(change gaps to dots)

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.

Publications and ongoing projects

Ongoing projects

  1. with W. Kubiś, Borel sets with perfect rectangles.
  2. with A. Martínez-Celis, P. Koszmider, Constructions of strongly rigid Boolean algebras.
  3. with C. Brech, L. Zdomskyy, Strong Nikodym property of Boolean algebras.
  4. with P. Borodulin-Nadzieja, Measures in the random model.
  5. with L. Zdomskyy, Convergence of measures after adding a real.

In preparation

  1. with P. Borodulin-Nadzieja, On sequences of homomorphisms into measure algebras.
  2. with L. Zdomskyy, A note on Semadeni's theorem.
  3. with W. Marciszewski, The Josefson-Nissenzweig theorem and filters on omega.
  4. with L. Zdomskyy, Minimally generated Boolean algebras with the Nikodym property.
  5. Grothendieck C(K)-spaces of small density.

Published or submitted

  1. Convergence of measures on Boolean algebras and cardinal characteristics of the continuum, 2020, preprint, submitted.
  2. with J. Kąkol, W. Marciszewski, L. Zdomskyy, On complemented copies of the space c0 in spaces Cp(X×Y), 2020, preprint, submitted.
  3. with J. Kąkol, L. Zdomskyy, The Josefson-Nissenzweig theorem, Grothendieck property, and finitely supported measures on compact spaces, 2020, preprint, submitted.
  4. with L. Zdomskyy, Convergence of measures in forcing extensions, Israel J. Math. 232 (2019), no. 2, 501-529, preprint.
  5. with L. Zdomskyy, The Nikodym property in the Sacks model, Topol. Appl. 230C (2017), 24-34, DOI, preprint.
  6. 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.
  7. Families of sets related to Rosenthal's lemma, Arch. Math. Logic 58 (2019), no. 1, 53-69, DOI, preprint.
  8. The Nikodym property and cardinal characteristics of the continuum, Ann. Pure Appl. Logic 170 (2019), no. 1, 1-35, DOI, preprint.
  9. with G. Plebanek, Countable tightness in the spaces of regular probability measures, Fund. Math. 229:2 (2015), 159-169, DOI, arXiv.
  10. 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.