Previous talks this semester:
19.12.2023, Tuesday 3pm, room 403
Damian Sobota (Kurt Gödel Research Center)
Title: On convergence of finitely supported measures and filters on ℕ.
Abstract:
For a free filter F on ℕ we write NF=ℕ∪{F} and endow this space with
the standard topology: points of ℕ are isolated and the neighborhoods of F are
all sets of the form A∪{F} for A in F. Spaces NF can be considered as
the simplest non-discrete Tychonoff spaces. During the talk we will investigate
for which filters F the spaces NF carry sequences (μn)n∈ℕ of finitely supported
signed measures with norm 1 and such that μn(f) converges to 0 for every real-valued bounded
continuous f on N_F. We show, among others, that this is the case, e.g.,
if and only if the dual ideal F* is Katetov below the ideal of all sets of asymptotic
density zero. We present some applications to Banach spaces of the form C(K). (Joint work with Witold Marciszewski.)
12.12.2023, Tuesday 3pm, room 403
Piotr Koszmider (IM PAN)
Title: Combinatorial set theory in noncommutative applications. Continuation.
5.12.2023, Tuesday 3pm, room 403
Piotr Koszmider (IM PAN)
Title: Combinatorial set theory in noncommutative applications. Continuation.
28.11.2023, Tuesday 3pm, room 403
Piotr Koszmider (IM PAN)
Title: Combinatorial set theory in noncommutative applications. Continuation.
7.11.2023, Tuesday 3pm, room 403
Piotr Koszmider (IM PAN)
Title: Combinatorial set theory in noncommutative applications.
Abstract:
In this series of talks we plan to discuss the revelation of combinatorial set-theoretic phenomena
in the noncommutative mathematics. This will include introducing and motivating and checking the details
of the very basics
of this theory (we assume no knowledge of operator algebras or C*-algebras from the participants).
We will attempt to focus on concrete combinatorial issues (and not on general algebraic theory) like the passage
from ultrafilters to quantum filters, from Boolean algebras and nonmetrizable compact totally disconnected
set-theoretic topology to real rank zero and AF nonseparable C*-algebras or the impact of additional set-theoretic axioms.
Like in Boolean algebras, general topology and measure theory in the classical period one could see
in C*-algebras (aka operator algebras) one of the modern central notions where the set-theoretic
methods can make difference.
The following two texts are characteristic of such an approach and will be exploited during the
talks:
(1) I. Farah, E. Wofsey,
Set theory and operator algebras. In
Cummings, James (ed.) et al., Appalachian set theory 2006--2012.
London Mathematical Society Lecture Note Series 406, 63--119 (2013).
(2) I. Farah, Combinatorial set theory of C*-algebras.
Springer Monographs in Mathematics. (2019);
24.10.2023, Tuesday 3pm, room 403
Zdeněk Silber (IM PAN)
Title: The Johnson-Lindenstrauss space and property (E). Continuation
17.10.2023, Tuesday 3pm, room 403
Zdeněk Silber (IM PAN)
Title: The Johnson-Lindenstrauss space and property (E).
Abstract: "The Johnson-Lindenstrauss space defined over an uncountable almost disjoint family A
is the Banach space JL(A) which has been used to provide many counterexamples in Banach space theory.
In the talk, we indroduce the construction of JL(A) and show some of its properties,
with special focus on the properties (E) and (E'), which are convex variants of having weak* Frechet-Urysohn dual ball
and weak* sequential dual ball respectively.
Specifically, we show that if A is maximal then the dual ball of JL(A) is never
Frechet-Uryshon in the weak* topology. On the other hand, for any almost disjoint family A,
the dual ball of JL(A) has weak* sequential dual ball (and hence JL(A) has property (E')).
The situation with property (E) is more complicated, as it depends on other properties of the
almost disjoint family A then just its maximality.
We show a result of Avilés, Martínez-Cervantes and Rodríguez that,
under CH, there are two maximal almost disjoint families A and B, such that JL(A)
does have property (E) and JL(B) does not.
This gives us a consistent example, that none of the implications
"weak* FU dual ball" implies (E) implies (E') can be reversed."
10.10.2023, Tuesday 3pm, room 403
Jesús Castillo (Universidad de Extremadura)
Title: Words and the twisting of C(K)-spaces.
Abstract: "Does a Banach space know if it is separable?"
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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