Tutorial Track

V. Fischer: Combinatorial sets of reals, definability and spectra

Infinitary combinatorial sets of reals, such as almost disjoint families, cofinitary groups, independent families, and towers occupy a central place in the study of the set-theoretic properties of the real line. Of particular interest are such extremal sets of reals, i.e. combinatorial sets which are maximal under inclusion with respect to a desired property, as well as their projective complexity and possible cardinalities. Moreover, this line of investigation is closely connected with the development of a broad spectrum of forcing techniques. In the tutorial we will discuss some recent advances in the subject and point towards interesting remaining open questions.

J. Hubička: TBA

M. Sabok: Hyperfinite graphs

In this tutorial, we will start with an introduction to hyperfinite graphs defined on probability spaces and then discuss several combinatorial problems arising in the setting of measurable combinatorics and measured group theory.

In particular, we will discuss the existence of measurable perfect matchings in hyperfinite graphs and we will see that bipartite graphs that are regular and one-ended always admit such perfect matchings. we will give some applications of the latter results to equidecomposition problems, such as the measurable circle squaring, and the existence of factors of iid perfect matchings in finitely generated groups.

O. Zindulka: TBA

Research Track

SpeakerTitleAbstract/Slides
Szymon Żeberski
Aleksander CieślakTBA
Michał GodziszewskiSpectrum of maximal almost orthogonal families in the Calkin algebraabstract
Jerzy KąkolOn $\Delta$-spaces $X$ and their characterization in term of spaces $C_{p}(X)$
Yurii KhomskiiTBA
Marlene Koelbing
Adam MartonTBA
Łukasz Mazurkiewicz
Marcin Michalski
Rahman MohamamdpourCertain Compactness Below $\aleph_\omega$
Lorenzo NotaroTree-representations of Borel functions in the Baire space
Beatrice PittonBorel and Borel^* sets in generalized descriptive set theoryabstract
Salvatore ScampertiTBA
Damian SobotaConvergence of measures and filters on $\omega$
Jarosław SwaczynaContinuity of coordinate I-projections via large cardinals
Corey SwitzerThe Special Tree Number
Agnieszka WidzSpecial families of magic sets
Wolfgang Wohofsky
Jindrich ZapletalColoring algebraic hypergraphs

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