Previous talks this semester:
19. 03. 2026 at 1.15 pm. Room 403.
Małgorzata Rojek (UW/IMPAN)
Around decompositions of C(N*)
Abstract: A closed subspace Y of a Banach space is called
complemented if there exists a closed subspace Z of X such that any
element x from X can be uniquely written as a sum of a vector from Y and a vector form Z.
In such case we say that X has a direct sum decomposition X = Y⊕Z.
A Banach space X is primary if for any direct sum decomposition
X = Y⊕Z at least one of the summands Y or Z is isomorphic to X.
During the talk, we will discuss certain properties of complemented subspaces
and decompositions of the Banach space C(N*), where N*=βN-N
is the Čech-Stone reminder of N.
We will show that in any direct sum decomposition of C(N*)
at least one of the summands contains a closed subspace isomorphic to C(N*).
Under CH, we will show that C(N*) is isomorphic to
l∞(C(N*)) and that C(N*) is primary.
The talk is mostly based on the article
"On the primariness of the Banach space l∞/c0" by L. Drewnowski and J. W. Roberts.
12. 03. 2026 at 1.15 pm. Room 403.
Piotr Koszmider (IMPAN)
Minimal extensions of Boolean algebras and the Efimov Problem
Abstract: We will discuss the notion of a minimal extension
of a Boolean algebra and minimally generated Boolean algebras (obtained by transfinite
sequence of consecutive minimal extensions). The Stone spaces of such algebras do not contain
the Cech-Stone compactification βN of the integers. We will show how to
construct such space which aditionally does not have nontrivial convergent sequences
in the Cohen model. This is related to the Efimov problem: does
every compact space either contain a copy of βN or a nontrivial convergent sequence.
It is still not known if the positive solution of this problem is consistent.
5. 03. 2026 at 1.15 pm. Room 403.
Piotr Koszmider (IMPAN)
On covers and tilings of infinite dimensional Banach spaces
Abstract: A body in a Banach space is a set which is the
closure of its interior. A tiling is a cover by bodies which may intersect only at their boundaries.
We will discuss classical and recent results concerning covers
and tilings of infinite dimensional Banach spaces. Some of the results depend on
the properties of the cardinals which are the densities of the spaces, other results
depend on the minimal cardinality of a pairwise disjoint family of closed sets which cover
the interval [0,1] (known to have its value dependent on additional set theoretic hypotheses).
Talks in the first semester of 2025-26.
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.
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