Working group in applications of set theory

impan seminar:

working group in applications of set theory

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."

Previous talks this semester:

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)
Piotr Koszmider (IM PAN)
Kacper Kucharski (PH. D. student UW)
Juliusz Pham (PH. D. student UW/IMPAN)
Małgorzata Rojek (PH. D. student UW/IMPAN)
Kamil Ryduchowski (PH. D. student UW/IMPAN)
Adam Skalski (IMPAN)
Przemysław Wojtaszczyk (IM PAN)

Forthcoming talks:

10.04.2025 Kamil Ryduchowski will continue.
17.04.2025 No seminar due to Easter break.
24.04.2025 No seminar
1.05.2005 No seminar due to International Worker's Day.
8.05.2025 Kacper Kucharski will speak on a construction by Dow, Junilla and Pelant of a compact scattered space K such that the Banach space C(K) is weakly pcc (every point finite family of open sets in the weak topology is countable). Apparently this C(K) is the only known in ZFC Banach space of density not exceeding the continuum which does not admit a fundamental biorthogonal system.