Previous talks this semester:
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 settheoretic 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
settheoretic topology to real rank zero and AF nonseparable C*algebras or the impact of additional settheoretic 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 settheoretic
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 20062012.
London Mathematical Society Lecture Note Series 406, 63119 (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 JohnsonLindenstrauss space and property (E). Continuation
17.10.2023, Tuesday 3pm, room 403
Zdeněk Silber (IM PAN)
Title: The JohnsonLindenstrauss space and property (E).
Abstract: "The JohnsonLindenstrauss 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* FrechetUrysohn 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
FrechetUryshon 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, MartínezCervantes 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 202223.
Talks in the first semester of 202223.
Talks in the second semester of 202122.
Talks in the first semester of 202122.
Talks in the second semester of 202021.
Talks in the first semester of 202021.
Talks in the second semester of 201920.
Talks in the first semester of 201920.
Talks in the second semester of 201819.
Talks in the first semester of 201819.
Talks in the second semester of 201718.
Talks in the first semester of 201718.
Talks in the second semester of 201617.
Talks in the first semester of 201617.
Talks in the second semester of 201516.
Talks in the first semester of 201516.
Talks in the second semester of 201415.
Talks in the first semester of 201415.
Talks in the second semester of 201314.
Talks in the first semester of 201314.
Talks in the second semester of 201213.
Talks in the first semester of 201213.
Talks in the second semester of 201112.
Talks in the first semester of 201112.
