impan seminar:

working group in applications of set theory



May 5, 2016, 1115-13, room 105, Przemysław Ohrysko (Ph. D. student, IM PAN)

Title: The Gelfand space of the measure algebra.
Abstract: In this talk I would like to present some recent results concerning the Banach algebra M(T) of Borel regular measures on the circle group with the convolution product. Since it is well-known that the spectrum of a measure can be much bigger then the closure of the values of its Fourier-Stieltjes transform (the Wiener-Pitt phenomenon) it is natural to ask what kind of topological properties of the Gelfand space Ge(M(T)) are responsible for this unusual spectral behaviour. It follows immediately from the existence of the Wiener-Pitt phenomenon that the set Z identified with Fourier-Stieltjes coefficients is not dense in Ge(M(T)). However, it is not clear if any other countable dense subset of this space exists. During my talk, I will disprove this fact - i.e. I will show the non-separability of the Gelfand space of the measure algebra on the circle group. This result is contained in a paper 'On topological properties of the measure algebra on the circle group' written in a collaboration with Michał Wojciechowski which has not been published yet but is available on arxiv.org with identifier: 1603.05864.

Previous talks this semester:

April 28, 2016, 1115-13, room 105, Tomasz Kochanek (IMPAN/UW)

Title: The Szlenk power type of injective tensor products of Banach spaces.
Abstract: We shall discuss the notion of the Szlenk power type (strictly related to the Szlenk index) and its relationships with asymptotic geometry of Banach spaces. In particular, we will describe how the so-called tree maps and subsequential tree estimates can be used as tools to understand the dynamics of the Szlenk derivations. Next, we will prove a formula for the Szlenk power type of the injective tensor product of Banach spaces with the Szlenk index at most ω (a joint result with S. Draga). This allows us, for example, to determine the moduli of asymptotic smoothness of the spaces of compact operators between lp-spaces.


April 21, 2016, 1115-13, room 105, Gonzalo Martínez Cervantes (Ph. D, student, Murcia)

Title: Riemann integrability versus weak continuity.
Abstract: We introduce some properties of Banach spaces related with Riemann integrability and we study the relation between weak-continuity and Riemann integrability. In particular, a Banach space is said to have the weak Lebesgue property if every Riemann integrable function from the unit interval into it is weakly continuous almost everywhere. We present several results concerning the weak Lebesgue property.


April 7, 2016, 1115-13, room 105, Tomasz Żuchowski (Ph. D. student, UWr)

Title: Nonseparable growth of N supporting a strictly positive measure.
Abstract: We will construct in ZFC a compactification γN of N such that its remainder γN\N is not separable and carries a strictly positive measure, i.e. measure positive on all nonempty open subsets. Moreover, the measure on our space is defined by the asymptotic density of subsets of N. Our remainder is the Stone space of some Boolean subalgebra of the algebra Bor(2N) of all Borel subsets of 2N containing all clopen sets. This line of research is motivated by the problem of characterizing the Banach spaces c0⊆ X⊆ l such that the space c0 is complemented in X.











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.

Time and place: Thursdays 11.15-13.00 am, room 105, 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:

  • Gonzalo Martínez Cervantes (Ph. D student, Murcia)
  • Saeed Ghasemi (IM PAN)
  • Rafał Górak (PW)
  • Clayton Suguio Hida (Ph. D. student, São Paulo)
  • Tomasz Kochanek (IM PAN/UW)
  • Piotr Koszmider (IM PAN)
  • Maciej Malicki (SGH)
  • Witold Marciszewski (UW)
  • Przemysław Ohrysko (Ph. D. student, IM PAN)
  • Eva Pernecká (IM PAN)
  • Jan Rozendaal (IM PAN)
  • Damian Sobota (Ph. D. student, IM PAN)
  • Todor Tsankov (Paris 7)
Forthcoming talks :

  • 05.05 Przemysław Ohrysko (Ph. D. student, IM PAN), new results on the Gelfand space of the measure algebra
  • 12.05 Maciej Malicki (SGH) on amenable groups
  • 19.05 Gonzalo Martínez Cervantes (Ph. D student, Murcia) on weakly Radon-Nikodym compacta
  • 26.05 Corpus Christi (holiday) no talk