impan seminar:

working group in applications of set theory





30.10 at 3.15 pm. Room 403

Kamil Ryduchowski (UW/IMPAN)
"On the existence and the form of uncountable biorthogonal systems in nonseparable C(K) spaces"

Abstract: "In this talk we shall use Todorcevic's Construction Schemes to consistently construct a nonmetrizable compact space K such that the Banach space C(K) has no uncountable biorthogonal systems. The space K, which we call a split Cantor set, will be obtained from the Cantor set by successively splitting ω1 points into two".




Previous talks this semester:


23.10 at 3.15 pm. Room 403

Małgorzata Rojek (UW/IMPAN)
"Almost disjoint families and some automorphic and injective properties of l∞/c0. Continuation."

Abstract: This week we will be dealing with extending isomorphisms between subspaces to automorphisms of the whole space. Using an old result of Bourgain and Tzafriri concerning finite dimensional Banach spaces we will prove that under MA(σ-linked) every isomorphism between two copies of c0(ω1) (for κ < 2ω) in l∞/c0 can be extended to an automorphism of l∞/c0. The talk is based on a joint paper with Piotr Koszmider and is a continuation of two talks from the last week, however, it can also be attended independently.



16.10 at 3.15 pm. Room 403

Małgorzata Rojek (UW/IMPAN)
"Almost disjoint families and some automorphic and injective properties of l∞/c0"

Abstract: "The question whether any isomorphism between two isomorphic copies of c0(ω1) in l∞/c0 can be extended to an automorphism of the whole space was posed by A. Aviles, F. Cabello Sanchez, J. Castillo, M. Gonzalez and Y. Moreno. The answer to this problem turns out to be independent of ZFC.

We will study embeddings and non-embeddings of spaces c0(ω1) and l∞c(κ) into l∞/c0 and of certain Boolean algebras into the algebra P(N)/Fin. Examination of such embeddings was used to prove the negative consistency result in the aforementioned problem and led to a number of open problems. The talk is based on a joint paper with Piotr Koszmider and is a continuation of the talk at the “Topology and set theory seminar" at MIM UW on 15.10, however, it can also be attended independently".






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 15.15-17.00 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)
  • Kacper Kucharski (PH. D. student UW)
  • Małgorzata Rojek (PH. D. student UW/IMPAN)
  • Kamil Ryduchowski (PH. D. student UW/IMPAN)
  • Krzysztof Zakrzewski (SGH)
Forthcoming talks:

  • 6.11. Kamil Ryduchowski will continue.
  • 13.11. Piotr Koszmider will speak.
  • 20.11. Piotr Koszmider will continue.