impan seminar:

working group in applications of set theory





12. 03. 2026 at 1.15 pm. Room 403.

Piotr Koszmider (IMPAN)
Minimal extensions of Boolean algebras and the Efimov Problem


Abstract: We will discuss the notion of a minimal extension of a Boolean algebra and minimally generated Boolean algebras (obtained by transfinite sequence of consecutive minimal extensions). The Stone spaces of such algebras do not contain the Cech-Stone compactification βN of the integers. We will show how to construct such space which aditionally does not have nontrivial convergent sequences in the Cohen model. This is related to the Efimov problem: does every compact space either contain a copy of βN or a nontrivial convergent sequence. It is still not known if the positive solution of this problem is consistent.




Previous talks this semester:


5. 03. 2026 at 1.15 pm. Room 403.

Piotr Koszmider (IMPAN)
On covers and tilings of infinite dimensional Banach spaces


Abstract: A body in a Banach space is a set which is the closure of its interior. A tiling is a cover by bodies which may intersect only at their boundaries. We will discuss classical and recent results concerning covers and tilings of infinite dimensional Banach spaces. Some of the results depend on the properties of the cardinals which are the densities of the spaces, other results depend on the minimal cardinality of a pairwise disjoint family of closed sets which cover the interval [0,1] (known to have its value dependent on additional set theoretic hypotheses).






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 13.15-15.00 pm, room 403, Śniadeckich 8




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:

  • Piotr Koszmider (IM PAN)
  • Małgorzata Rojek (PH. D. student UW/IMPAN)
  • Jan Rossa (M. A. student UW)
  • Kamil Ryduchowski (PH. D. student UW/IMPAN)
  • Piotr Szewczak (MIM UW)
  • Krzysztof Zakrzewski (SGH)
Forthcoming talks:

  • 19.03 Małgorzata Rojek will talk on some properties of C(N*), where N*=βN-N is the Čech-Stone reminder of N.

  • 26.03 Małgorzata Rojek will continue.

  • 2.04 No talks due to the Easter break.

  • 9.04. Michał Wojciechowski will talk about compact spaces with Nevanlina-Pick property and the Gelfand spaces of Banach algebras.

  • 16.04 Kacper Kucharski will continue his talk from Wednesday seminar on Cp(K) space not isomorphic to its square.

  • 23.04 Jarosław Swaczyna (Łódź University of Technology) will talk about versions of bases in Banach spaces where instead of the usual convergence one considers the I-convergence, where I is an ideal in P(N) (e.g., analytic, P-ideal, maximal etc.)

  • 30. 04 J. Swaczyna will continue.

  • 7.05 ?

  • 14.05 Antonio Acuaviva (Ph.D. student of Lancaster University)

  • 21. 05?

  • 28.05 No talk.

  • 4. 06 ?

  • 11.06 ?