Previous talks this semester:
October 20, 2016, 10^{15}12, no seminar due to Scientific Council of the Institute,
instead we invite the participants of the seminar to the Doctoral defence (in Polish) of
Damian Sobota (IM PAN) at 11.15 on 19.10, room 106. The title of the thesis written under the guidance of
Piot Koszmider is "Cardinal invariants of the continuum and
convergence of measures on compact spaces.
October 12, 2016, 15^{15}17, room 403, Saeed Ghasemi (IM PAN)
Title: "An introduction to scattered C*algebras"  Continuation
Abstract:
"The techniques and constructions of compact, Hausdorff
scattered spaces, or equivalently (by the Stone duality) superatomic
Boolean algebras, have been used in the literature of Banach spaces
for many fundamental results in the forms of Banach spaces C(K), or
more generally Asplund spaces. Scattered C*algebras were introduced
as C*algerbas which are Asplund as Banach spaces. However, the
analogues of the commutative tools and constructions were not
developed for these C*algebras. In a joint work with Piotr Koszmider (S. Ghasemi, P.
Koszmider; Noncommutative CantorBendixson
derivatives and scattered C*algebras)
we investigated these tools and constructions parallel to the ones in
settheoretic topology. I will introduce the CantorBendixson
derivatives for C*algebras, obtained by using the ideal generated by
the minimal projections of these algebras, and present some of the
basic properties of these ideals. I will also show how these notions
can be used to construct exotic C*algebras. In particular, I will
show the existence of a nonseparable AFalgebra which is an inductive
limit of stable AFideals, yet it has no maximal stable ideal."
October 5, 2016, 15^{15}17, room 403, Saeed Ghasemi (IM PAN)
Title: "An introduction to scattered C*algebras"
Abstract:
"The techniques and constructions of compact, Hausdorff
scattered spaces, or equivalently (by the Stone duality) superatomic
Boolean algebras, have been used in the literature of Banach spaces
for many fundamental results in the forms of Banach spaces C(K), or
more generally Asplund spaces. Scattered C*algebras were introduced
as C*algerbas which are Asplund as Banach spaces. However, the
analogues of the commutative tools and constructions were not
developed for these C*algebras. In a joint work with Piotr Koszmider (S. Ghasemi, P.
Koszmider; Noncommutative CantorBendixson
derivatives and scattered C*algebras)
we investigated these tools and constructions parallel to the ones in
settheoretic topology. I will introduce the CantorBendixson
derivatives for C*algebras, obtained by using the ideal generated by
the minimal projections of these algebras, and present some of the
basic properties of these ideals. I will also show how these notions
can be used to construct exotic C*algebras. In particular, I will
show the existence of a nonseparable AFalgebra which is an inductive
limit of stable AFideals, yet it has no maximal stable ideal."
September 27, 2016, 15^{15}17, room 106, Piotr Koszmider (IM PAN)
Title: "A nonseparable scattered C*algebra without
a nonseparable commutative subalgebra"
Abstract:
"This talk is based on a paper T. Bice, P. Koszmider, A note on the AkemannDoner and FarahWofsey constructions,
To appear in PAMS where we removed an additional assumption of the continuum hypothesis from a previous
construction of Akemann and Doner of an algebra like in the title (A nonseparable C*algebra with only separable abelian C*subalgebras.
Bull. London Math. Soc. 11 (1979), no. 3, 279–284). The main combinatorial "trick" is to use Luzin's almost disjoint family,
so first, we will describe this notion."
September 20, 2016, 15^{15}17, room 106, Tristan Bice (IM PAN/WCMCS)
Title: "Locally Compact Stone Duality"
Abstract:
"Almost all wellstudied real rank zero C*algebras can be constructed from inverse semigroups.
We focus on just the first part of this construction, where a zero dimensional compact (Hausdorff)
topological space comes from Exel's tight spectrum of the idempotent semilattice.
First we show how this can be generalized to a kind of Stone duality between separative posets
and 'pseudobases' of zero dimensional locally compact spaces.
This is closely related to a wellknown set theoretic construction of a Boolean algebra from a poset.
Next, we consider bases of general locally compact spaces, how these can be axiomatized and how the space can be reconstructed as a generalized Stone space.
Time permitting, we will outline how this should allow more general (e.g. projectionless)
C*algebras to be constructed from inverse semigroups."
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.
