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Weekly research seminar
2023-11-29, 16:15, 5050
Maciej Malicki (IM PAN)
Compacta and their homeomorphism groups from posets
Very recently A. Bartoš, T. Bice and A. Vignati discovered a duality, generalizing the Stone duality, between second countable T_1 compacta and graded omega-posets. Their approach allows for elementary combinatorial constructions, in the spirit of Fraïssé theory, of classical cont...
2023-11-22, 16:15, 5050
Jindrich Zapletal (University of Florida)
Fraenkel-Mostowski models revisited
A dynamical ideal is a group G acting on a set X, together with an ideal I on X invariant under the action. A dynamical ideal comes with an associated model of ZF set theory. I will discuss several theorems which connect dynamical properties of the ideal with fragments of axiom of choice in the asso...
2023-11-08, 16:15, 5050
David Chodounsky (Institute of Mathematics of the Czech Academy of Sciences)
Games for chromatic numbers of analytic graphs
We define games which characterize countable coloring numbers of analytic graphs on Polish spaces. These games can provide simple verification of the countable chromatic number of certain graphs. We also get a simpler proof of a dichotomy originally proved by Adams and Zapletal: if an analytic graph...
2023-10-25, 16:15, 5050
Tomasz Kochanek (University of Warsaw)
Operator semigroups in the Calkin algebra, part 2
The abstract of the talk can be found here: https://drive.google.com/file/d/1xCTvKwjFXONxqUN1NurltvhGewn6GyV7/view?usp=sharing ...
2023-10-18, 16:15, 5050
Tomasz Kochanek (University of Warsaw)
Operator semigroups in the Calkin algebra
The abstract of the talk can be found here: https://drive.google.com/file/d/1aMk2GrPJTYMP8PiMOKgJU4Hay5186G5s/view?usp=sharing ...
2023-10-11, 16:15, 5050
Jesús M. F. Castillo (Universidad de Extremadura)
2023-06-14, 16:15, 5050
Jakub Andruszkiewicz (Doctoral School of Exact and Natural Sciences UW)
Cofinalities of the symmetric group and of the ultrapowers of ω
We consider the following cardinal invariants of the continuum: cf(Sym(ω)), being the cofinality of the group of permutations of ω, and mcf, defined as the minimal cofinality of an ultrapower of ω over any non-principal ultrafilter. During the talk we will present known results regarding the rela...
2023-05-31, 16:15, 5050
Piotr Koszmider (IM PAN)
Ramsey properties of the distance on nonseparable spheres
Given a nonseparable metric space (M,d) bounded by 2 we consider (A) dichotomies D_r for r in (0,2): either there is uncountable subset N of M such that d(x, y) > r for all distinct x,y in N or else M is the union of countably many sets each of diameter not bigger than r; (B) the metric...
2023-05-24, 16:15, 5050
Grzegorz Plebanek (University of Wrocław)
Countable discrete extensions of compact lines
We consider a separable compact line K and its extension L consisting of K and a countable number of isolated points. The main object of study is the existence of a bounded extension operator E: C(K) -> C(L). We show that if such an operator exists then there is one which norm is an odd natural n...
2023-05-10, 16:15, Zoom
Aristotelis Panagiotopoulos (Carnegie Mellon University)
Menger continua via projective Fraïssé theory
Projective Fraïssé theory was introduced by T.Irwin and S.Solecki as a natural framework for analyzing the dynamics of homeomorphism groups of compact metrizable spaces in terms of finite combinatorics. In this talk I will provide some basic background in projective Fraïssé t...
