# Double session at Fields Institute (D. Bartosova and A. Rinot)

Place: Fields Institute, Room 210

Date: 17-October- 2014

Time: 12:30-15:00

Speaker 1 (from 12:30 to 13:30): Dana Bartosova
Title: Finite Gowers’ Theorem and the Lelek fan
Abstract: The Lelek fan is a unique non-degenrate subcontinuum of the Cantor fan with a dense set of endpoints. We denote by $G$ the group of homeomorphisms of the Lelek fan with the compact-open topology. Studying the dynamics of $G$, we generalize finite Gowers’ Theorem to a variety of operations and show how it applies to our original problem. This is joint work with Aleksandra Kwiatkowska.
___________________________________________________________
Speaker 2 (from 13:30 to 15:00): Assaf Rinot
Title: Productivity of higher chain condition
Abstract: We shall survey the history of the study of the productivity of the k-cc in partial orders, topological spaces, and Boolean algebras. We shall address a conjecture that tries to characterize such a productivity in Ramsey-type language. For this, a new oscillation function for successor cardinals, and a new characteristic function for walks on ordinals will be proposed and investigated.