Thursday, 01.03. 2018, 10:15, room 105, Wieslaw Kubis (Czech Academy and UKSW)
"On the weak amalgamation property "
Abstract: "The somewhat technical weak amalgamation property (weak AP) of
models with embeddings was identified first by Ivanov in 1999 during
his study of generic automorphisms, later re-discovered by Kechris and
Rosendal (2007), again studying generic automorphisms. Recently, we have
discovered, jointly with Adam Krawczyk, that the weak amalgamation
property plays essential role in characterizing the existence of a
winning strategy in the abstract Banach-Mazur game, played with models
and embeddings. We shall describe the main results relating this game
with the weak AP. Next, we shall present some new examples of hereditary
classes of finite structures with the weak AP, failing its stronger
version called the cofinal AP. The material comes from joint works with
A. Krawczyk, A. Kruckman, and A. Panagiotopoulos.".
Time and place: Thursdays 10.15-12.00 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:
- Tristan Bice (IM PAN/WCNM)
- Michał Tomasz Godziszewski (Ph. D. student IMPAN)
- Tomasz Kochanek (IM PAN/UW)
- Piotr Koszmider (IM PAN)
Forthcoming talks :
- 08.03.2018 ?
- 15.03.2018 Piotr Koszmider
will talk about diamond "constructions schemes" proposed recently by Todorcevic (S. Todorcevic,
A construction scheme for non-separable structures. Adv. Math. 313 (2017), 564–589.) and some applications.
- 22.03.2018 Tomasz Kochanek
will talk about Fernandez-Polo's and Peralta's proof of Pfitzner's theorem concerning a characterization of
weakly compact sets in the dual space to a C*-algebra.