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Weekly research seminar
Organizers
- prof. dr hab. Witold Marciszewski
- prof. dr hab. Piotr Zakrzewski
Information
Wednesdays, 4:15 p.m. , room: 5050Research fields
List of talks
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May 12, 2021, 4:15 p.m.
Piotr Koszmider (Institute of Mathematics of the Polish Academy of Sciences)
Pure states, quantum filters and ultrafilters
We will describe how the usual notion of an ultrafilter on N extends to the notion of a maximal quantum filter. Such objects correspond to pure states of quantum systems the same way that ultrafilters …
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May 5, 2021, 4:15 p.m.
Jakub Andruszkiewicz (University of Warsaw)
Shelah's proof of diamond
It is a well-known fact that the diamond principle implies CH, but the reverse implication does not hold. The situation for successor cardinals larger than the first uncountable cardinal is quite different - as proved …
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April 28, 2021, 4:15 p.m.
Piotr Zakrzewski (University of Warsaw)
On countably perfectly meager sets
We study a strengthening of the notion of a perfectly meager set. We say that that a subset A of a perfect Polish space X is countably perfectly meager in X if for every sequence …
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April 21, 2021, 4:15 p.m.
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 …
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April 14, 2021, 4:15 p.m.
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 …
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March 24, 2021, 4:15 p.m.
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 …
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March 17, 2021, 4:15 p.m.
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 …
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March 10, 2021, 4:15 p.m.
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 …
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March 3, 2021, 4:15 p.m.
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 …
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Jan. 27, 2021, 4:15 p.m.
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 …
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Jan. 20, 2021, 4:15 p.m.
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 …
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Jan. 13, 2021, 4:15 p.m.
Rafał Filipów (University of Gdańsk)
If I were a rich density
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 …
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Dec. 16, 2020, 4:15 p.m.
Wiesław Kubiś (Cardinal Stefan Wyszyński University in Warsaw and Institute of Mathematics of the Czech Academy of Sciences)
The weak Ramsey property
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 …
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Dec. 9, 2020, 4:15 p.m.
Antonio Aviles Lopez (Universidad de Murcia)
The category of Banach lattices
We shall review some recent developments in the study of the category of Banach lattices: Free, projective, injective objects, etc. Analogies and differences with Banach spaces will be highlighted. This is part of joint works …
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Dec. 2, 2020, 4:15 p.m.
Piotr Szewczak (Cardinal Stefan Wyszyński University in Warsaw)
Abstract colorings, games and ultrafilters
During the talk we consider various kinds of Ramsey-type theorems. Bergelson and Hindman investigated finite colorings of the complete graph [N]^2 with vertices in natural numbers, involving an algebraic structure of N. It follows from …
