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Tea Seminar of our groupPlace and time:
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In this seminar, guests and members of our group present their research, or topics of interest to us. Presently we use a hybrid format for the seminar (in-person and zoom). In case you are interested, please contact Linus Kramer.
Talks:
- 21.10.2024 Maneesh Thakur (Delhi) Real elements in groups
- 28.10.2024 Jonas Pinke (Münster) A category theoretical proof of Pontryagin's duality theorem
- 18.11.2024 Judit Jansat Ballarín (Münster) Just infinity and profinite rigidity of Coxeter groups
- 25.11.2024 Marco Sthefano Amelio (Münster) An overview of Small Cancellation Theory
- 09.12.2024 Eduardo Silva (Münster) Entropy, Poisson boundaries and wreath products
- 13.01.2025 Hannah Boss (Münster) HNN-extensions of hyperbolic groups
- 20.01.2025 Benjamin Brück (Münster)
Abstract: In a group, a real element is an element which is conjugate to its inverse. These elements may or may not exist in a given group. We will discuss this notion and mention some of its aspects, its connections with some other branches of mathematics. We also will discuss the case of algebraic groups and some results on the structure of real elements in such groups, mention some open questions in the area. The talk should be understandable to anyone with background in basic group theory and linear algebra.
Abstract: Pontryagin's famous duality theorem establishes a strong relationship between locally compact abelian hausdorff (LCA) groups and their dual groups, providing deep insights into the structure and behavior of these groups. In the talk we will give a proof of the duality theorem based on ideas from category theory, which is guided by the structure within the category LCA.The duality theorem will first be established for the subcategory of compactly generated abelian Lie-Groups.Through the study of "formal" limits and colimits the duality is expanded to a duality between the subcategories of discrete abelian and compact abelian LCA groups. From there, a study of exact sequences will result in the full duality theorem for the category LCA.
Abstract: Just infinite Coxeter groups are precisely the irreducible affine Coxeter groups. This result serves as a key tool to establish that irreducible affine Coxeter groups are profinitely rigid within the class of all Coxeter groups. Furthermore, this rigidity extends to all affine Coxeter groups. To achieve this generalization, we replace the just infinite condition with an analysis of the relationship between finite normal subgroups of Coxeter groups and those of their profinite completions, ultimately reducing the problem to affine Coxeter groups without finite normal subgroups.
Abstract: Let G be a group and R a set of elements of G with normal closure N. In general, it is not easy to understand the quotient G/N. Small Cancellation Theory is, broadly speaking, a family of conditions of the following form: Let G be a negatively curved group, R a family of ‘independent enough’ elements. Then G/N is itself negatively curved, and we understand many properties of this quotient. In this talk, I will review the classical Small Cancellation Theory, as well as some of its variants (Graphical Small Cancellation and Geometric Small Cancellation), and exhibit some of the groups with exotic properties that can be constructed using these methods.
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