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Cotygodniowe seminarium badawcze
2021-04-21, godz. 16:15, Zoom
Piotr Borodulin-Nadzieja (University of Wrocław)
On forcing names for ultrafilters
We show a way to handle names for ultrafilters in the random forcing. Using this approach we reprove Kunen's theorem about long towers in the random model and Kamburelis' characterization of Boolean algebras supporting finitely additive measures. The talk represents joint works with Dami...
2021-04-14, godz. 16:15, Zoom
Ziemowit Kostana (University of Warsaw)
What would the rational Urysohn space and the random graph look like if they were uncountable?
We apply the technology developed in the 80s by Avraham, Rubin, and Shelah, to prove that the following is consistent with ZFC: there exists an uncountable, separable metric space X with rational distances, such that every uncountable partial 1-1 function from X to X is an isometry on an uncountable...
2021-03-24, godz. 16:15, Zoom
Grzegorz Plebanek (University of Wrocław)
Weakly Radon-Nikodym Boolean algebras
Weakly Radon-Nikodym (WRN) Boolean algebras are named after a certain class of compacta related to Banach spaces but they can be charaterized as those algebras that have, in a sense, few independent sequences. We compare the class of WRN algebras with some others, such as minimally generated algebra...
2021-03-17, godz. 16:15, Zoom
Damian Głodkowski (University of Warsaw)
Coverings of Banach spaces and their subsets by hyperplanes
A hyperplane of a Banach space is a closed one-codimensional subspace. Hyperplanes are nowhere dense and so, no countable collection of hyperplanes can cover the entire space. Given a Banach space we consider the \sigma-ideal of all of its subsets which are covered by countably many hyperplanes and ...
2021-03-10, godz. 16:15, Zoom
Piotr Koszmider (Institute of Mathematics of the Polish Academy of Sciences)
A Banach space induced by an almost disjoint family, admitting only few operators and decompositions
We consider the closed linear subspace X(A) of the Banach space of real bounded sequences (l_infinity) generated by sequences converging to zero (c_0) and the characteristic functions of elements of an uncountable, almost disjoint family A of infinite subsets of N. This Banach spac...
2021-03-03, godz. 16:15, Zoom
Marcin Sabok (McGill University)
Probabilistic programming semantics for name generation
Abstract: I will discuss a recent result connecting the nu-calculus (which is an extension of simply-typed lambda calculus modelling the so-called "name generation") with a recent model for probabilistic programming, called the quasi-Borel spaces. There is a natural interpretation of the n...
2021-01-27, godz. 16:15, Zoom
Aleksandra Kwiatkowska (University of Wrocław)
The automorphism group of the random poset
A number of well-studied properties of Polish groups concern the interactions between the topological and algebraic structure of those groups. Examples of such properties are the small index property, the automatic continuity, and the Bergman property. An important approach for proving them is showi...
2021-01-20, godz. 16:15, Zoom
Adam Bartoš (Institute of Mathematics of the Czech Academy of Sciences)
Approximate Fraïssé theory and MU-categories
Fraïssé theory links together properties of families of structures like the amalgamation property with properties of limit objects like homogeneity and the extension property. The structures considered are not limited to be first-order structures, and the maps between the structures are ...
2021-01-13, godz. 16:15, Zoom
Rafał Filipów (University of Gdańsk)
Abstract upper densities are monotone and subadditive functions from the power set of positive integers into the unit real interval that generalize the upper densities used in number theory, including the upper asymptotic density, the upper Banach density, and the upper logarithmic density. ...
2020-12-16, godz. 16:15, Zoom
Wiesław Kubiś (Cardinal Stefan Wyszyński University in Warsaw and Institute of Mathematics of the Czech Academy of Sciences)
We show how to extend the Kechris-Pestov-Todorcevic correspondence to categories with weak amalgamations, where extreme amenability is tested for the automorphism group of the generic limit, taken with a suitable topology. We characterize extreme amenability in terms of a Ramsey-like property of the...
