March 2016

# Aleksandra Kwiatkowska: Universal flows and Ramsey theory

18/03/16 19:01

Tuesday, March 22, 2016 17:15

*Room:*D1-215*Aleksandra Kwiatkowska*

Speaker:Speaker:

*Title*: Universal flows and Ramsey theory*Abstract*. The subject lies on the crossroad of topological dynamics, topology, topological groups and Ramsey theory. We will present Kechris-Pestov-Todorcevic theorem about connections between structural Ramsey theory, extremely amenable groups and universal minimal flows. We will show some examples. Next, we will focus on groups of homeomorphisms (Cantor set, Lelek fan, pseudoarc, Hilbert cube). We will recall known results and ask some questions.# Tomasz Żuchowski: Nonseparable growth of omega supporting a strictly positive measure

14/03/16 18:57

Tuesday, March 15, 2016 17:15

Our remainder is a Stone space of a Boolean subalgebra of Lebesgue measurable subsets of \(2^{\omega}\) containing all clopen sets.

*Room:*D1-215*Tomasz Żuchowski*

Speaker:Speaker:

*Title*: Nonseparable growth of omega supporting a strictly positive measure*Abstract*. We will construct in ZFC a compactification \(\gamma\omega\) of \(\omega\) such that its remainder \(\gamma\omega\backslash\omega\) is not separable and carries a strictly positive measure, i.e. measure positive on nonempty open subsets. Moreover, the measure on our space is defined by the asymptotic density of subsets of \(\omega\).Our remainder is a Stone space of a Boolean subalgebra of Lebesgue measurable subsets of \(2^{\omega}\) containing all clopen sets.

# Piotr Borodulin-Nadzieja: Mathias forcings for slaloms

08/03/16 10:16

Tuesday, March 8, 2016 17:15

*Room:*D1-215*Piotr Borodulin-Nadzieja*

Speaker:Speaker:

*Title*: Mathias forcings for slaloms*Abstract*. We will show an example of a Boolean algebra which is not sigma-centered but sigma-n-linked. Moreover, it has property (*) of Fremlin. Such examples were known before. We will construct our algebra using Mathias forcing for something resembling the density filter.