impan seminar:

working group in applications of set theory



September 27, 2016, 1515-17, 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 Akemann-Doner and Farah-Wofsey 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, 279284). The main combinatorial "trick" is to use Luzin's almost disjoint family, so first, we will describe this notion."



Previous talks this semester:


September 20, 2016, 1515-17, room 106, Tristan Bice (IM PAN/WCMCS)

Title: "Locally Compact Stone Duality"
Abstract: "Almost all well-studied 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 well-known 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 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.

SPECIAL NONCOMMUTATIVE SEMESTER

During the fall semester 2016/17 the seminar is devoted to applictaions of set theory in noncommutative mathematics. This is a part of satellite events to Simons semester: Noncommutative geometry the next generation which takes place at IM PAN during this semester.

Time and place: Thursdays 10.15-12.00 am, room 105, Sniadeckich 8

Due to lecture courses at Simon's semester temporary time and place of the seminar is Tuesdays 15.15-17.00, room 106, Sniadeckich 8

The scope of the seminar: Set-theoretic combinatorial and topological methods in diverse fields of mathematics, with a special emphasis on abstract analysis like Banach spaces, Banach algebras, C*-algebras, Here we include both the developing of such methods as forcing, descriptive set theory, Ramsey theory as well as their concrete applications in the fields mentioned above.

Working group style: We will make efforts so that this seminar has more a working character rather than the presentation style. This means that we encourage long digressions, discussions, background preparations and participation of everyone. We would like to immerse ourselves into the details of the mathematical arguments studied. Also the talks are usualy devoted to research in progress or fascinating results leading to some project not yet resolved. While ready final results could be presented at other seminars at IM PAN or UW.

Participants this semester so far:

  • Tristan Bice (WCNM/IM PAN)
  • Saeed Ghasemi (WCNM/IM PAN)
  • Clayton Suguio Hida (Ph. D. student, São Paulo)
  • Tomasz Kochanek (IM PAN/UW)
  • Piotr Koszmider (IM PAN)
  • Tomasz Żuchowski (Ph. D. student, Wrocław/WCNM)
Forthcoming talks :

  • 05.10.2016, 1515-17, room 403, Saeed Ghasemi (IMPAN)
    Introduction to scattered C*-algebras
  • 12.10.2016, 1515-17, room 403, TBA
  • 20.10.2016, 1515-17, no seminar due to Scientific Council of the Institute, instead we invite the participants of the seminar to the Doctoral defence of Damian Sobota (IM PAN) at 11.15 on 19.10. The title of the thesis written under the guidance of Piot Koszmider is "Cardinal invariants of the continuum and convergencce of measures on compact spaces. The room and the language of the defence will be announced later.
  • Following seminars will take place on Thursdays at 10.15-12.