Dana Bartošová: Attempts to understand the universal minimal flow of \(\mathbb{Z}\times\mathbb{Z}\)
10/12/20 19:55
Tuesday, December 15, 2020 17:00
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Dana Bartošová (University of Florida)
Title: Attempts to understand the universal minimal flow of \(\mathbb{Z}\times\mathbb{Z}\)
Abstract: Every \(\mathbb{Z}\)-flow on a compact Hausdorff space \(X\) can be interpreted as a homeomorphism \(f : X \to X\) and its forward and backward iterates. A flow is minimal if every orbit is dense. The universal minimal flow \(M(\mathbb{Z})\) maps continuously onto every minimal flow while preserving the action, and it is unique up to isomorphism. The purpose of this project is to understand \(M(\mathbb{Z} \times \mathbb{Z})\) in terms of \(M(\mathbb{Z})\). We will start with the few results that are out there about the connection between the corresponding Čech-Stone compactifications \(\beta (\mathbb{Z}\times\mathbb{Z})\) and \(\beta (\mathbb{Z})\) by Hindman, Blass, and Blass and Moche, that are useful in our considerations. This is a joint work with Ola Kwiatkowska.
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Dana Bartošová (University of Florida)
Title: Attempts to understand the universal minimal flow of \(\mathbb{Z}\times\mathbb{Z}\)
Abstract: Every \(\mathbb{Z}\)-flow on a compact Hausdorff space \(X\) can be interpreted as a homeomorphism \(f : X \to X\) and its forward and backward iterates. A flow is minimal if every orbit is dense. The universal minimal flow \(M(\mathbb{Z})\) maps continuously onto every minimal flow while preserving the action, and it is unique up to isomorphism. The purpose of this project is to understand \(M(\mathbb{Z} \times \mathbb{Z})\) in terms of \(M(\mathbb{Z})\). We will start with the few results that are out there about the connection between the corresponding Čech-Stone compactifications \(\beta (\mathbb{Z}\times\mathbb{Z})\) and \(\beta (\mathbb{Z})\) by Hindman, Blass, and Blass and Moche, that are useful in our considerations. This is a joint work with Ola Kwiatkowska.