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Tee-Seminar der AG KramerZeit und Ort:
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Inhalt:
Mitglieder der Arbeitsgruppe und Gäste tragen über ihre laufenden Forschungsarbeiten vor, oder über Themen, die uns interessieren. Wenn Sie am Seminar über ZOOM teilnehmen möchten, schicken Sie bitte eine e-mail an Dr. Varghese.
Vorträge:
- 21.04.2020 Lara Beßmann (Münster) Discreteness in Universal Groups
- 28.04.2020 Daniel Keppeler (Münster) Automatic continuity for groups with torsion
- 05.05.2020 Yuri Santos Rego (Magdeburg) Twisted conjugacy in arithmetic groups
- 12.05.2020 Nils Leder (Münster) Automorphism groups of graph products and property FA
- 19.05.2020 Bakul Sathaye (Ben Gurion University) Nonhyperbolic groups with Menger curve boundary
- 26.05.2020 Olga Varghese (Münster) Coxeter groups and Kazhdan's property (T)
- 09.06.2020 Jonas Flechsig (Bielefeld) Braids and Artin groups
- 16.06.2020 Pieter Senden (KU Leuven) The R∞ property for RAAGs and graph products
- 30.06.2020 Jens Bossaert (Ghent University) Expanding the universe of universal groups
- 07.07.2020 Corina Ciobotaru Classical homogeneous dynamics in a non-linear setting
Abstract: In 2000, Burger and Mozes defined the concept of a universal group acting on a tree with prescribed local actions, providing interesting examples of totally disconnected locally compact groups. In recent developments their foundational construction has been generalised in various ways: Simon Smith studied the topological properties in a more relaxed setting (where the local actions are not assumed to be transitive or of finite degree), Adrien Le Boudec introduced "almost-universal" groups (where one allows for a controlled number of singularities), and Tom De Medts, Ana Silva and Koen Struyve generalised the original notion of universal groups to the realm of right-angled buildings. We will discuss why right-angled buildings are a natural setting, try to unify these approaches, and study how the permutational properties of the local groups and the combinatorics of the diagram affect the topological properties of the resulting groups.
The automorphisms group of a bi-regular tree contains a rich class of non-linear subgroups G that still share the good properties of the linear ones. Given that, classical questions from homogeneous dynamics can be examined and proved. For example, if H is a discrete subgroup of G, recent results show there is a classification of ergodic probability measures on G / H that are invariant under horospherical subgroups. When H is moreover a cocompact lattice, the horospherical action is uniquely ergodic. Or when H is a geometrically finite lattice quantitative recurrence and equidistribution related to the above probability measures on G / H hold true. This is a joint project with Vladimir Finkelshtein and Cagri Sert.