impan seminar:

working group in applications of set theory





22.10. 2026 at 10.15 am. Room 106.

Piotr Szewczak (MIM UW)
"Filters on omega with combinatorial and topological properties".


Abstract: We will discuss filters on the natural numbers with the Menger and Hurewicz covering properties. We will present methods for constructing such filters, including constructions from sets of reals with the corresponding property in all finite powers. We will discuss the characterization of Menger filters as strong P-plus filters and explain how the Menger and Hurewicz properties are reflected in the behavior of the associated Mathias forcing. The talk will also address selected open problems.




Previous talks this semester:


15.10. 2026 at 10.15 am. Room 106.

Grzegorz Wełyczko (PWr)
"On the existence of universal compact Hausdorff spaces".


Abstract: We study universal spaces in the class of compact Hausdorff spaces of weight at most the continuum, where a space is called universal if every space in the class is its continuous image. We will show that, under the Continuum Hypothesis, the Čech-Stone remainder of the natural numbers is universal for this class. We will then present a strengthening of a consistency result of Dow and Hart, who showed that the nonexistence of such a universal space is consistent with ZFC. Namely, we will show that it is consistent with ZFC that no family of fewer than 22ω spaces in this class is jointly universal: there is always a space in the class that is not a continuous image of any member of the family. Finally, we will explain why this bound is optimal.



8.10. 2026 at 10.15 am. Room 106.

Piotr Koszmider (IMPAN)
An Efimov space in the Cohen model.


Abstract: A compact Hausdorff space is called an Efimov space if it contains neither a nontrivial convergent sequence nor a copy of βN. Whether such a space can be constructed in ZFC remains a longstanding open problem. We will describe a (mostly folklore) construction of an Efimov space in a Cohen model, emphasizing the main combinatorial ideas and the way Cohen forcing is used to destroy all potential convergent sequences. The proof is via the Stone duality, i.e., we construct the Boolean algebra of all clopen subsets of the space.




Talks in the second semester of 2025-26.

Talks in the first semester of 2025-26.

Talks in the second semester of 2024-25.

Talks in the first semester of 2024-25.

Talks in the second semester of 2023-24.

Talks in the first semester of 2023-24.

Talks in the second semester of 2022-23.

Talks in the first semester of 2022-23.

Talks in the second semester of 2021-22.

Talks in the first semester of 2021-22.

Talks in the second semester of 2020-21.

Talks in the first semester of 2020-21.

Talks in the second semester of 2019-20.

Talks in the first semester of 2019-20.

Talks in the second semester of 2018-19.

Talks in the first semester of 2018-19.

Talks in the second semester of 2017-18.

Talks in the first semester of 2017-18.

Talks in the second semester of 2016-17.

Talks in the first semester of 2016-17.

Talks in the second semester of 2015-16.

Talks in the first semester of 2015-16.

Talks in the second semester of 2014-15.

Talks in the first semester of 2014-15.

Talks in the second semester of 2013-14.

Talks in the first semester of 2013-14.

Talks in the second semester of 2012-13.

Talks in the first semester of 2012-13.

Talks in the second semester of 2011-12.

Talks in the first semester of 2011-12.

Time and place: Thursdays 10.15-12.00, room 106, Śniadeckich 8



Organizers: Piotr Koszmider (IMPAN) and Piotr Szewczak (MIM UW)


The scope of the seminar: Set-theoretic combinatorial and topological methods in diverse fields of mathematics, with a special emphasis on abstract analysis like Banach spaces, Banach algebras, C*-algebras, Here we include both the developing of such methods as forcing, descriptive set theory, Ramsey theory as well as their concrete applications in the fields mentioned above.

Working group style: We will make efforts so that this seminar has more a working character rather than the presentation style. This means that we encourage long digressions, discussions, background preparations and participation of everyone. We would like to immerse ourselves into the details of the mathematical arguments studied. Also the talks are usualy devoted to research in progress or fascinating results leading to some project not yet resolved. While ready final results could be presented at other seminars at IM PAN or UW.

Participants this semester so far:

  • Bartosz Kamiński (M.A. student Lodz UT)
  • Marta Kładź-Duda (PH. D. student UW)
  • Piotr Koszmider (IM PAN)
  • Jacek Krajczok (IM PAN)
  • Kacper Kucharski (PH. D. student UW)
  • Małgorzata Rojek (PH. D. student UW/IMPAN)
  • Jan Rossa (PH. D. student UW)
  • Kamil Ryduchowski (PH. D. student UW/IMPAN)
  • Piotr Szewczak (MIM UW)
  • Maksymilian Wesoły (PH. D. student UW)
  • Agnieszka Widz (IM PAN)
  • Tomasz Żuchowski (IM PAN)
Forthcoming talks:

  • 29.10 Tomasz Żuchowski will speak on constructions of ideals an algebras related to hypergraphs.
  • 5.11 Kacper Kucharski will speak on a partion of the Cantor set into two sets, one rigid and the other homogeneous.
  • 12.11 No seminar.
  • 19.11 Małgorzata Rojek
  • 26.11 Małgorzata Rojek