impan seminar:

working group in applications of set theory



June 25 at 10.45-12.45, Room 106. Maciej Malicki (IM PAN); Representations of oligomorphic groups

Abstract: We will talk about a recent paper by Todor Tsankov devoted to continuous unitary representations of oligomorphic permutation groups. A Polish group G of permutations of the natural numbers N is called oligomorphic if the natural action of G on the product N^n has only finitely many orbits for every n. These groups include the full permutation group of N, the automorphism group of the countable dense linear order, the homeomorphism group of the Cantor space, etc. Oligomorphic groups have also strong connections with model theory: the automorphism group of a countable model M of a theory T over a countable language is oligomorphic iff T is omega-categorical. In the paper, a complete classification of irreducible representations of oligomorphic groups is presented. As an application, it is proved that many oligomorphic groups have Kazhdan's property (T).

Previous talks this semester:

May 14 at 12.00, Room 105. Michał Wojciechowski (IM PAN) and Przemysław Ohrysko.

Abstract: We will sum up the cycle of seminars devoted to the measure algebra with a panel discussion


April 16 at 12.00, Room 105. Przemysław Ohrysko.

Abstract: I'm going to talk on paper "Spectra of independent power measures" published by W. J. Bailey, G. Brown and W. Moran. As the title says it is concentreted on studying spectral properties of measures which have independent convolution powers. Proofs of main results use generalized characters and relays on some kind of extensions conncected to them. The most important theorem which will be proved states that if continous measure has independent convolution powers then its spectrum is whole spectral disc. The latter can be applied to classical examples of singular measures such as Riesz products.

April 9 at 12.00, Room 105. Przemysław Ohrysko.

Abstract: I'm going to talk on paper "Spectra of independent power measures" published by W. J. Bailey, G. Brown and W. Moran. As the title says it is concentreted on studying spectral properties of measures which have independent convolution powers. Proofs of main results use generalized characters and relays on some kind of extensions conncected to them. The most important theorem which will be proved states that if continous measure has independent convolution powers then its spectrum is whole spectral disc. The latter can be applied to classical examples of singular measures such as Riesz products.


March 26 at 12.00, Room 105. Piotr Koszmider; Remarks on representations of the bidual to C(T).

Abstract: Continuing our attempts of understanding the space of multiplicative functionals on M(T) (the measure algebra on the circle with convolution) with the weak* topology we will present some classical results concerning the representation of the bidual of C(T) as some C(K). We will also discuss another representation due to Mauldin which assumes CH: D. Mauldin, A representation theorem for the second dual of C[0,1]. Studia Math. 46 (1973), 197 - 200.


March 19. at 12.00, Room 105. Piotr Koszmider; Remarks on representations of the bidual to C(T).

Abstract: Continuing our attempts of understanding the space of multiplicative functionals on M(T) (the measure algebra on the circle with convolution) with the weak* topology we will present some classical results concerning the representation of the bidual of C(T) as some C(K).








Talks in the first semester of 2012-13.

Talks in the second semester of 2011-12.

Talks in the first semester of 2011-12.

Time and place: Tuesdays 12.00- 14.00, room 105, Sniadeckich 8

The scope of the seminar: Set-theoretic methods in diverse fields of mathematics, in particular in Banach spaces, C*-algebras, topology, the structure of the real line, measure theory, Boolean algebras, topological groups. 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. To achive this, the duration of the seminar will not be rigidly fixed and may reach even 3 hours with the breaks. We would like to immerse ourselves into the details of the mathematical arguments studied. We hope that such a seminar may complement presentations at the Wednesday set theory seminar at the University of Warsaw.

Participants this semester:

  • Lendro Candido (USP)
  • Tomasz Kohanek (UŚ)
  • Piotr Koszmider (IM PAN)
  • Mikołaj Krupski (Ph. D. student IMPAN)
  • Maciej Malicki (IM PAN)
  • Witold Marciszewski (UW)
  • Przemysław Ohrysko (Ph. D. student IM PAN)
  • Diana Ojeda (Pd. D. student Cornell U.)
  • Marcin Sabok (IM PAN)
  • Michał Wojciechowski (IM PAN)
Forthcoming talks:


  • April and May: We moved talks of the visitors working on Banach spaces and set theory to the Functional Analysis Seminar at 3 pm (9.04 and 16.04)
  • June 25 and 27 at 10.45: M.Malicki/M.Sabok