impan seminar:

working group in applications of set theory





12.12.2024 at 2.15 pm. ROOM CHANGE TO 106.
Piotr Koszmider (IMPAN).
On the existence of universal uniform Eberlein compacta and universal Hilbert generated Banach spaces. Continuation.

Abstract: "A compact Hausdorff space K is said to be uniform Eberlein (UEC) if it embeds into a Hilbert space with the weak topology. A Banach space X is said to be Hilbert generated (HG) if there is a bounded linear operator from a Hilbert space into X with its range dense in X. In this series of talks we will review classical results of Benyamini, Rudin and Wage concerning these spaces like the fact that if a Banach space X is HG, then the dual ball BX* with the weak* topology is a UEC or that K is a UEC if and only if C(K) is HG. Then we will prove that the existence of a UEC of weight continuum which continuously maps onto all UECs of weight continuum as well as the existence of a HG space of density continuum which contains isomorphic/isometric copies of all HG spaces of density continuum are independent from the axioms of ZFC. The results concerning the universal objects are from M. Bell, Universal uniform Eberlein compact spaces. Proc. Am. Math. Soc. 128, No. 7, 2191-2197 (2000) and C. Brech, P. Koszmider, On universal spaces for the class of Banach spaces whose dual balls are uniform Eberlein compacts. Proc. Am. Math. Soc. 141, No. 4, 1267-1280 (2013)."




Previous talks this semester:


5.12.2024 at 2.15 pm. Room 403.
Piotr Koszmider (IMPAN).
On the existence of universal uniform Eberlein compacta and universal Hilbert generated Banach spaces. Continuation.



28.11 at 2.15 pm. Room 403.
Zdeněk Silber (IMPAN).
The Separable Quotient Problem for Cp spaces.

Abstract: "There is a famous open problem in Banach space theory whether every infinite-dimensional Banach space admits an infinite-dimensional separable quotient. For some classes of Banach spaces, including reflexive spaces or C(K) spaces, the answer is known to be positive. Variants of this problem for the classes of general topological vector spaces or locally convex topological vector spaces are known to have negative answer. In this talk we focus on the class of Cp(K) spaces of continuous functions on a compact space K equipped with the topology of pointwise convergence. While the separable quotient problem for these spaces is still open, there are some results regarding necessary conditions on K for Cp(K) to not have an infinite-dimensional separable quotient. We will present the result of Kąkol and Śliwa that if Cp(K) does not admit an infinite-dimensional separable quotient, then K needs to be an Efimov space, that is, K cannot contain a convergent sequence or a copy of βN".



7.11 at 2.15 pm. Room 403.
Piotr Koszmider (IMPAN).
On the existence of universal uniform Eberlein compacta and universal Hilbert generated Banach spaces

Abstract: "A compact Hausdorff space K is said to be uniform Eberlein (UEC) if it embeds into a Hilbert space with the weak topology. A Banach space X is said to be Hilbert generated (HG) if there is a bounded linear operator from a Hilbert space into X with its range dense in X. In this series of talks we will review classical results of Benyamini, Rudin and Wage concerning these spaces like the fact that if a Banach space X is HG, then the dual ball BX* with the weak* topology is a UEC or that K is a UEC if and only if C(K) is HG. Then we will prove that the existence of a UEC of weight continuum which continuously maps onto all UECs of weight continuum as well as the existence of a HG space of density continuum which contains isomorphic/isometric copies of all HG spaces of density continuum are independent from the axioms of ZFC. The results concerning the universal objects are from M. Bell, Universal uniform Eberlein compact spaces. Proc. Am. Math. Soc. 128, No. 7, 2191-2197 (2000) and C. Brech, P. Koszmider, On universal spaces for the class of Banach spaces whose dual balls are uniform Eberlein compacts. Proc. Am. Math. Soc. 141, No. 4, 1267-1280 (2013)."



24.10 at 2.15 pm. Room 403.
Małgorzata Rojek (IMPAN/MIMUW).
The non-separability of the Gelfand space of the measure algebra on the circle. Continuation..


17.10 at 2.15 pm. Room 403.
Małgorzata Rojek (IMPAN/MIMUW).
The non-separability of the Gelfand space of the measure algebra on the circle.

Abstract: "In this series of two talks we will study the Gelfand space of the algebra M(T) of measures on the circle. Although the space arises in a very natural way, there are still many open questions concerning its topology. During the first talk we will recall basic properties of the algebra M(T) and introduce some useful tools, in particular the Riesz products. The main goal of the second talk is to prove that the Gelfand space Δ(M(T)) contains continuum pairwise disjoint open sets".


10.10, 2.30pm, room 321
The public defence of doctoral thesis of Damian Głodkowski.

The thesis is entitled "Some applications of set theory in Banach spaces and operator algebras". For more details see https://www.impan.pl/instytut/awanse/materialy-publiczne/doktor/damian-glodkowski/ogloszenie-o-publicznej-obronie.pdf







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)
  • Arkady Leiderman (BGU Beer-Sheva)
  • 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)
  • Zdeněk Silber (IM PAN)
  • Michał Wojciechowski (IM PAN)
  • Przemysław Wojtaszczyk (IM PAN)
Forthcoming talks:

  • 19.12. No seminar.
  • 9.01 Juliusz Pham will talk on generalized characters on the measure algebra.
  • No seminar due to the Winter School
  • 23.01 Juliusz Pham will continue.