April 2021
Szymon Żeberski: Applications of non-measurable unions
27/04/21 04:53
Tuesday, April 27, 2021 17:00
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Szymon Żeberski
Title: Applications of non-measurable unions
Abstract: Using a game-theoretic approach (Set-Cover game) we obtain a generalization of the classical result of Brzuchowski, Cichoń, Grzegorek and Ryll-Nardzewski on non-measurable unions. We will present applications of this result to establishing some countability and continuity properties of measurable functions and homomorphisms between topological groups.
It is a joint work with Taras Banakh and Robert Rałowski https://arxiv.org/abs/2011.11342.
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Szymon Żeberski
Title: Applications of non-measurable unions
Abstract: Using a game-theoretic approach (Set-Cover game) we obtain a generalization of the classical result of Brzuchowski, Cichoń, Grzegorek and Ryll-Nardzewski on non-measurable unions. We will present applications of this result to establishing some countability and continuity properties of measurable functions and homomorphisms between topological groups.
It is a joint work with Taras Banakh and Robert Rałowski https://arxiv.org/abs/2011.11342.
Aristotelis Panagiotopoulos: The definable content of (co)homological invariants: Cech cohomology
14/04/21 11:44
Tuesday, April 20, 2021 17:00
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Aristotelis Panagiotopoulos (University of Munster)
Title: The definable content of (co)homological invariants: Cech cohomology
Abstract: In this talk we will develop a framework for enriching various classical invariants of homological algebra and algebraic topology with additional descriptive set-theoretic information. The resulting "definable invariants" can be used for much finer classification than their purely algebraic counterparts. We will illustrate how these ideas apply to the classical Cech cohomology invariants to produce a new "definable cohomology theory" which, unlike its classical counterpart, it provides a complete classification to homotopy classes of mapping telescopes of d-tori, and for homotopy classes of maps from mapping telescopes of d-tori to spheres. In the process, we will develop several Ulam stability results for quotients of Polish abelian non-archimedean groups G by Polishable subgroups H. A special case of these rigidity results answer a question of Kanovei and Reeken regarding quotients of the \(p\)-adic groups.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Aristotelis Panagiotopoulos (University of Munster)
Title: The definable content of (co)homological invariants: Cech cohomology
Abstract: In this talk we will develop a framework for enriching various classical invariants of homological algebra and algebraic topology with additional descriptive set-theoretic information. The resulting "definable invariants" can be used for much finer classification than their purely algebraic counterparts. We will illustrate how these ideas apply to the classical Cech cohomology invariants to produce a new "definable cohomology theory" which, unlike its classical counterpart, it provides a complete classification to homotopy classes of mapping telescopes of d-tori, and for homotopy classes of maps from mapping telescopes of d-tori to spheres. In the process, we will develop several Ulam stability results for quotients of Polish abelian non-archimedean groups G by Polishable subgroups H. A special case of these rigidity results answer a question of Kanovei and Reeken regarding quotients of the \(p\)-adic groups.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
Witold Marciszewski: On zero-dimensional subspaces of Eberlein compacta
12/04/21 17:02
Tuesday, April 13, 2021 17:00
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Witold Marciszewski (University of Warsaw)
Title: On zero-dimensional subspaces of Eberlein compacta
Abstract: Let us recall that a compact space K is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology. Our talk will be devoted to the known problem of the existence of nonmetrizable compact spaces without nonmetrizable zero-dimensional closed subspaces. Several such spaces were obtained using some additional set-theoretic assumptions. Recently, P. Koszmider constructed the first such example in ZFC. We investigate this problem for the class of Eberlein compact spaces. We construct such Eberlein compacta, assuming the existence of a Luzin set. We also show that it is consistent with ZFC that each Eberlein compact space of weight greater than \(\omega_1\) contains a nonmetrizable closed zero-dimensional subspace.
The talk is based on the paper "On two problems concerning Eberlein compacta": http://arxiv.org/abs/2103.03153
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Witold Marciszewski (University of Warsaw)
Title: On zero-dimensional subspaces of Eberlein compacta
Abstract: Let us recall that a compact space K is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology. Our talk will be devoted to the known problem of the existence of nonmetrizable compact spaces without nonmetrizable zero-dimensional closed subspaces. Several such spaces were obtained using some additional set-theoretic assumptions. Recently, P. Koszmider constructed the first such example in ZFC. We investigate this problem for the class of Eberlein compact spaces. We construct such Eberlein compacta, assuming the existence of a Luzin set. We also show that it is consistent with ZFC that each Eberlein compact space of weight greater than \(\omega_1\) contains a nonmetrizable closed zero-dimensional subspace.
The talk is based on the paper "On two problems concerning Eberlein compacta": http://arxiv.org/abs/2103.03153