impan seminar:

working group in applications of set theory





23.04.2024, Tuesday 10.15, room 403

Kamil Ryduchowski (UW/IMPAN)

Title: GNS representations and pure states - continuation

Abstract: We will continue our investigation of GNS representations induced by pure states. We will start by proving that a GNS representation induced by a pure state is irreducible, which will finish the proof of the theorem discussed last week. Then we will use our knowledge collected during this series of talks to obtain some corollaries concerning pure states and a bit more general representations.




Previous talks this semester:





16.04.2024, Tuesday 10.15, room 403

Kamil Ryduchowski (UW/IMPAN)

Title: GNS representations and pure states

Abstract: In the last meeting we discussed the GNS construction of a representation of a C*-algebra, where a given state of a C*-algebra corresponds to a vector state of the representing operator algebra. In this talk we will study the behaviour of that construction in the case when the given state is a pure state.



9.04.2024, Tuesday 10.15, room 403

Kamil Ryduchowski (UW/IMPAN)

Title: GNS construction.

Abstract: We will present the classical GNS construction and will conclude the representation theorem for C*-algebras as operator algebras. The talk does not require any background beyond the presenations from the last fall.



26.03.2024, Tuesday 10.15, room 403

Damian Głodkowski (UW/IMPAN)

Title: A Boolean algebra with the Grothendieck property and without the Nikodym property under CH. Continuation.



19.03.2024, Tuesday 10.15, room 403

Damian Głodkowski (UW/IMPAN)

Title: A Boolean algebra with the Grothendieck property and without the Nikodym property under CH. Continuation.



12.03.2024, Tuesday 10.15, room 403

Damian Głodkowski (UW/IMPAN)

Title: A Boolean algebra with the Grothendieck property and without the Nikodym property under CH. Continuation.



5.03.2024, Tuesday 10.15, room 403

Damian Głodkowski (UW/IMPAN)

Title: A Boolean algebra with the Grothendieck property and without the Nikodym property under CH.

Abstract: In 1984 Talagrand, assuming the continuum hypothesis, gave an example of a Boolean algebra with the Grothendieck property and without the Nikodym property. In a series of talks I will present a construction of such a Boolean algebra that uses a modification of Talagrand's method. The constructed algebra consists of Borel subsets of the Cantor set satisfying certain symmetry property (we call such sets balanced). The talks will be based on the paper "Epic math battle of history: Grothendieck vs Nikodym" by D. Głodkowski and A. Widz, arXiv:2401.13145










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: Tuesdays 10.15-12.00 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 (PH.D. student UW/IMPAN)
  • Tomasz Kochanek (MIM UW)
  • Piotr Koszmider (IM PAN)
  • Kacper Kucharski (PH. D. student UW)
  • Kamil Ryduchowski (PH. D. student UW/IMPAN)
  • Zdeněk Silber (IM PAN)
  • Krzysztof Zakrzewski (PH.D. student UW)
Forthcoming talks :

  • 30.04 - no seminar
  • 7.05 - Kacper Kucharski will talk about compact Hausdorff spaces in the Cohen model.