Weekly research seminar

2021-01-13, 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, 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...

2020-12-09, 16:15, Zoom

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 with G. Martinez Cervantes, J. Rodriguez, J. D. Rodriguez Abellan, P. Trad...

2020-12-02, 16:15, Zoom

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 their result that for each finite coloring of [N]^2, there are f...

2020-11-25, 16:15, Zoom

Jan van Mill (University of Amsterdam)

We sketch the proof of the following result: the existence of a normal space whose modal logic coincides with the modal logic of the Kripke frame isomorphic to the power set of a two element set is equivalent to the existence of a measurable cardinal. Whether normal in this result can be weakened to...

2020-11-18, 16:15, Zoom

Lyubomyr Zdomskyy (Institut für Mathematik, Kurt Gödel Research Center, Universität Wien)

**Between the Pytkeev and Frechet-Urysohn properties of function spaces**In this talk we aim to compare the Frechet-Urysohn property and some of its formal weakenings for spaces of the form C_p(X). In particular, we plan to present a sketch of the construction under CH of a set of reals X such that C_p(X) has the Pytkeev property (i.e., for every subset A of C_p(X) co...

2020-11-04, 16:15, Zoom

Maciej Malicki (IMPAN)

**Non-locally compact Polish groups and non-essentially countable orbit equivalence relations**It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. In the talk, I will answer this question positively for the class of all Polish groups ...

2020-10-28, 16:15, Zoom

Taras Banakh (Ivan Franko National University of Lviv and UJK Kielce)

**Small uncountable cardinals in asymptology**In the talk we shall discuss some cardinal characteristics of the continuum that appear in large-scale topology, usually as the smallest weights of coarse structures that belong to certain classes (indiscrete, inseparable, large) of finitary or locally finite coarse structures on $\omega$. Besides w...

2020-03-11, 16:15, 5050

Ziemowit Kostana (University of Warsaw)

**Cohen-like poset for adding automorphisms of Fraisse limits**There exists a natural forcing notion which turns the set of integers into a Fraisse limit of a given Fraisse class. This long-known phenomenon provided a rough intuition that Fraisse limits, as "generic structures", have some connections with forcing. I investigate a version of this forcing, which ...

2020-03-04, 16:15, 5050

Witold Marciszewski (University of Warsaw)

**Complemented subspaces of function spaces C_p(X\times Y), sequences of measures, and ultrafilters**The result of Schachermayer and Cembranos asserts that, for a compact space K, the Banach space C(K) of continuous real valued maps on K, contains a complemented copy of the Banach space c_0 if and only if K admits a sequence of regular Borel measures which is weak* convergent, but not weakly conv...