Rigidity of group topologies and universal minimal flows (C05)

• Subject Area: Mathematics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 427320536

We will study automatic continuity and universal minimal flows for topological groups acting on geometric objects. First, we focus on rigidity of group topologies, motivated by a question due to Rosendal on the existence of a locally compact infinite group with the automatic continuity property. We want to study this question for Burger–Mozes groups. Furthermore, motivated by a question of Evans–Hubička–Nešetřil, we want to understand when universal minimal flows of kaleidoscopic groups are metrisable. Our methods will involve interactions between group theory, topological dynamics and Ramsey theory.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1442: Geometry: Deformations and Rigidity
• Applicant Institution: Universität Münster
• Project Head: Dr. Aleksandra Kwiatkowska, Ph.D.