December 2020
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.
Włodzimierz J. Charatonik: Projective Fraïssé limits of trees
03/12/20 11:17
Tuesday, December 8, 2020 17:00
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Włodzimierz J. Charatonik (Missouri University of Science and Technology)
Title: Projective Fraïssé limits of trees
Abstract: We continue study of projective Fraïssé limit developed by Irvin, Panagiotopoulos and Solecki. We modify the ideas of monotone, confluent, or retraction from continuum theory as well as several properties of continua so as to apply to topological graphs. As the topological realizations of the Fraïssé limits we obtain either some known continua, for example the dendrite \(D_3\) or the Cantor fan, or quite new, interesting ones for which we do not yet have topological characterizations.
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Włodzimierz J. Charatonik (Missouri University of Science and Technology)
Title: Projective Fraïssé limits of trees
Abstract: We continue study of projective Fraïssé limit developed by Irvin, Panagiotopoulos and Solecki. We modify the ideas of monotone, confluent, or retraction from continuum theory as well as several properties of continua so as to apply to topological graphs. As the topological realizations of the Fraïssé limits we obtain either some known continua, for example the dendrite \(D_3\) or the Cantor fan, or quite new, interesting ones for which we do not yet have topological characterizations.