impan seminar:

working group in applications of set theory





22.5.2025 at 2.15 pm. Room 403.
Kamil Ryduchowski (IMPAN/UW).
A short introduction to construction schemes II.

Abstract: "We will use construction schemes to obtain a coherent Suslin tree, i.e. a Suslin tree of the form T={fα|δ: δ<α<ω1}, where fα almost equals fβ|α for all α<β<ω1. In doing so we will present some useful functions connected to a construction scheme."




Previous talks this semester:




15.5.2025 at 2.15 pm. Room 403.
Luis David Reyes Sáenz (UNAM, México).
AD families, Alexandrov-Urysohn compacta, and Johnson-Lindenstrauss spaces.

Abstract: "The objective of the talk is to show how some combinatorial properties of almost disjoint (AD) families are translated into topological properties of the Alexandrov-Urysohn compactum, and, in turn, how those properties are translated into the space of continuos functions over this space; known as the Johnson-Lindenstrauss space. During the talk I will present a result due to Petr Simon on the existence a compact Frechet-Urysohn (FU) space such that its square is not FU, and show how this produces nontrivial examples of Banach spaces such that its dual ball is not FU. If time allows, I will also present some ongoing work with Michael Hrusak on a convex version of the FU property that follows this combinatorial into Banach spaces properties framework."



8.5.2025 at 2.15 pm. Room 403.
Arturo Antonio Martínez Celis Rodríguez (UWr).
A crumbly Radon-Nikodym compact space

Abstract: "A compact space K is Radon-Nikodym if there is a lower semi-continuous metric fragmenting K (equivalently K is a subspace of (BX*, w*) where vector measures with values in X* satisfy the Radon-Nikodym theorem). In this talk, we will show that, assuming an additional axiom called a parametrized diamond, it is possible to construct a crumbly compact Radon-Nikodym space, i.e., a compact Radon-Nikodym space with a continuous non-Radon-Nikodym image, of weight ℵ1."



10.4.2025 at 2.15 pm. Room 403.
Kacper Kucharski (MIM UW).
A ZFC example of a Banach space of density continuum without a fundamental biorthogonal system

Abstract: "During the talk we will construct a compact scattered space K of weight continuum such that the Banach space of continuous functions C(K) (of density continuum) does not have a fundamental biorthogonal system. This result of Dow, Junnila and Pelant complements the result of Todorcevic which says that PFA implies that any Banach space of density ω1 has a fundamental biorthogonal system."


3.4.2025 at 2.15 pm. Room 403.
Kamil Ryduchowski (IMPAN/MIM UW).
A short introduction to construction schemes I.

Abstract: "In this talk we will present the notion of construction schemes (with capturing properties), introduced by Todorcevic and existing e.g., under the diamond principle. They are combinatorial structures on ω1 resembling 2-cardinals (simplified morasses). They provide an alternative way of using the diamond in a fashion somewhat similar to forcing, as one can construct 'generic' objects by induction along the scheme. During the talk we shall discuss basic definitions regarding construction schemes and use them to construct a Suslin tree."


13.03.2025 at 2.15 pm. Room 403.
Damian Głodkowski (MIM UW).
Introduction to operator K-theory for the Calkin algebra and related structures. Continuation.



13.03.2025 at 2.15 pm. Room 403.
Damian Głodkowski (MIM UW).
Introduction to operator K-theory for the Calkin algebra and related structures. Continuation.



6.03.2025 at 2.15 pm. Room 403.
Damian Głodkowski (MIM UW).
Introduction to operator K-theory for the Calkin algebra and related structures.

Abstract: "We will introduce basic notions of K-theory for C*-algebras with special emphasis on the Calkin algebra (i.e., the algebra of bounded operators on a separable Hilbert space modulo the ideal of compact operators) and their relations to the Fredholm index theory. The motivation for our considerations is the problem of the existence of automorphisms of Calkin algebras that change the Fredholm index. It is known that the Open Coloring Axiom implies the non-existence of such automorphisms, but the problem remains open in ZFC. We will discuss possible approaches to the problem that combine the tools of set theory with K-theory".






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 14.15-16.00 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:

  • Tomasz Cieśla (MIM UW)
  • Damian Głodkowski (MIM UW)
  • Tomasz Kochanek (MIM UW)
  • Jan Kostrzoń (PH. D. student UW/IMPAN)
  • Piotr Koszmider (IM PAN)
  • Mikołaj Krupski (MIM UW)
  • Kacper Kucharski (PH. D. student UW)
  • Witold Marciszewski (MIM UW)
  • Juliusz Pham (PH. D. student UW/IMPAN)
  • Małgorzata Rojek (PH. D. student UW/IMPAN)
  • Kamil Ryduchowski (PH. D. student UW/IMPAN)
  • Luis David Reyes Sáenz (PH. D. student UNAM, México)
  • Adam Skalski (IM PAN)
  • Agnieszka Widz (PH.D. student Lodz UT)
  • Tomasz Weiss (UKSW)
  • Przemysław Wojtaszczyk (IM PAN)
Forthcoming talks:

  • 29.05. 2025 Juliusz Pham will talk about a construction of specific subspaces of the Gelfand space of the convolution measure algebras.
  • 5.06.2005 Luis David Reyes Sáenz will continue on AD families, Alexandrov-Urysohn compacta, and Johnson-Lindenstrauss spaces.