Previous talks this semester:
23.5.2023, Tuesday 10.15, room 403
Kacper Kucharski (MIM UW)
Title: Gaps in P(ω)/fin and their applications. Continuation.
Abstract: " In this series of two talks, we will discuss the
(non)existence of certain types of gaps in the Boolean algebra P(ω)/fin.
Specifically, we will demonstrate that there are no (κ, λ) - gaps for κ,
λ ≤ ω, and then construct a Hausdorff gap, i.e., an (ω1, ω1) - gap.
Additionally, we will present a characterisation of the bounding number
in terms of a Rothberger gap. Finally as an application, we will
use the Hausdorff gap to demonstrate the existence of a universal
measure zero set. All results mentioned above will be proven within ZFC.
In the end, we will also briefly discuss the notion of indestructible
gaps and describe the situation under PFA."
16.5.2023, Tuesday 10.15, room 403
Kacper Kucharski (MIM UW)
Title: Gaps in P(ω)/fin and their applications.
Abstract: " In this series of two talks, we will discuss the
(non)existence of certain types of gaps in the Boolean algebra P(ω)/fin.
Specifically, we will demonstrate that there are no (κ, λ) - gaps for κ,
λ ≤ ω, and then construct a Hausdorff gap, i.e., an (ω1, ω1) - gap.
Additionally, we will present a characterisation of the bounding number
in terms of a Rothberger gap. Finally as an application, we will
use the Hausdorff gap to demonstrate the existence of a universal
measure zero set. All results mentioned above will be proven within ZFC.
In the end, we will also briefly discuss the notion of indestructible
gaps and describe the situation under PFA.".
9.5.2023, Tuesday 10.15, room 403
Kamil Ryduchowski (MIM UW/IM PAN)
Title: An introduction to the combinatorics of 2-cardinals. Conclusion.
Abstract: "This is the last of the series of talks devoted to present applications of 2-cardinals (versions of Velleman's neat simplified morasses) to combinatorics. We will use 2-cardinals to
prove the existence of a version of the Hausdorff gap at level
κ (κ is a regular cardinal) and use the coloring defined from 2-cardinals (a version of Todorcevic's ρ function) to prove the existence of a κ+-Aronszajn tree".
25.4.2023, Tuesday 10.15, room 403
Kamil Ryduchowski (MIM UW/IM PAN)
Title: An introduction to the combinatorics of 2-cardinals. Continuation.
Abstract: "In this talk we will continue our study of 2-cardinals (versions of Velleman's simplified morasses).
We will use them to define a certain
κ-valued coloring on pairs of κ+ (κ is a cardinal) and a family of functions from κ+ to {0,1,2} with interesting combinatorial properties, which we will use to construct a κ-Kurepa tree
and a version of the Hausdorff gap at the level of κ".
18.4.2023, Tuesday 10.15, room 403
Kamil Ryduchowski (MIM UW/IM PAN)
Title: An introduction to the combinatorics of 2-cardinals.
Abstract: "This is the first of two talks devoted to presenting the notion
of a 2-cardinal (a version of Velleman's simplified morass) and its applications in infinitary combinatorics. Intuitively speaking, a 2-cardinal is a special family of subsets of κ+ (κ is a cardinal), each
of them of cardinality smaller than κ, which can be used to transfinite inductive constructions of objects of size
κ+ without dealing with the step of cofinality κ in the process.
In this talk we will present the definition of 2-cardinals, prove their basic properties
and use them to construct a κ-Kurepa tree and a version of the Hausdorff gap at the level of κ"
4.4.2023, Tuesday 10.15, room 403
Zdeněk Silber (IM PAN)
Title: On Corson's property (C) and other sequential properties.
Abstract: "In this talk we introduce convex variants of topological properties
like countable tightness, sequentiality, being Fréchet-Urysohn or sequential compactness,
when applied to the dual ball of a Banach space equiped with the weak* topology.
We will show some implications of those properties with a particular focus on
the equivalence (under PFA) of countable tightness and its convex variant, property (C)."
28.03.2023, Tuesday 10.15, room 403
Piotr Koszmider (IMPAN)
Title: Stepping-up with an Aronszajn tree and adding a Cohen real. Continuation.
Abstract: "We will discuss classical techniques involving almost coherent families of injections
from countable ordinals into ω and adding a Cohen real. Applications will include:
adding one Cohen real to any model produces a coloring with the Galvin property, Suslin tree
and an entangled set of reals etc."
21.03.2023, Tuesday 10.15, room 403
Krzysztof Zakrzewski (MIMUW)
Title: An elementary proof of the Eberlein-Smulian theorem. Continuation.
Abstract: "We will give a brief proof of the Eberlein-Smulian theorem
which says that for a subset of a Banach space endowed with the weak topology
three conditions are equivalent, namely: conditional compactness,
conditional sequential compactness and conditional countable
compactness. The proof will use standard results from theory of Banach
spaces, namely Alaoglu's theorem and the Hahn-Banach theorem.
The talk is based on the article "An Elementary Proof of
Eberlein-Smulian Theorem" by Robert Whitley (Math. Ann. 1967)"
14.03.2023, Tuesday 10.15, room 403
Krzysztof Zakrzewski (MIMUW)
Title: An elementary proof of the Eberlein-Smulian theorem.
Abstract: "We will give a brief proof of the Eberlein-Smulian theorem
which says that for a subset of a Banach space endowed with the weak topology
three conditions are equivalent, namely: conditional compactness,
conditional sequential compactness and conditional countable
compactness. The proof will use standard results from theory of Banach
spaces, namely Alaoglu's theorem and the Hahn-Banach theorem.
The talk is based on the article "An Elementary Proof of
Eberlein-Smulian Theorem" by Robert Whitley (Math. Ann. 1967)"
7.03.2023, Tuesday 10.15, room 403
Piotr Koszmider (IMPAN)
Title: Stepping-up with an Aronszajn tree and adding a Cohen real.
Abstract: "We will discuss classical techniques involving almost coherent families of injections
from countable ordinals into ω and involving adding a Cohen real. Applications will include:
The existence of a strong Luzin set implies the existence of a coloring of pairs of ω1
with very strong multidimensional antiramsey properties; adding one Cohen real to any model produces a Suslin tree
and produces an entangled set of reals etc."
Talks in the second 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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