Abstracts
22.10.2019, 15:00, WIL A 120: Seminar Geometrie
Jakub Gismatullin, University of Wroclaw: Quantitative approach to approximations by groups, w-sofic groups and some remarks on the Higman group
I will present a quantitative approach for the situation where a finitely generated (presented) group can be or cannot be approximated by a family of metric groups. Examples include perfect groups and solvable groups (via recent results of A.Thom, J. Schneider and N. Nikolov). In the second part of the talk I will speak about w-sofic groups in the sense of L. Glebsky and M. Rivera.
19.11.2019, 15:00, WIL A 120: Seminar Geometrie
Yuri Santos Rego, Universität Magdeburg: The matrix groups of H. Abels
The linear groups introduced by Herbert Abels in the late seventies gave the first counterexamples to a question asked by P. Hall in '54. Since then, Abels' groups served as test cases for a wide variety of investigations in infinite group theory, for instance regarding finiteness properties, asymptotic cones, C*-algebras, and more
recently permutation stability.
In this talk I will define Abels' groups (over arbitrary commutative rings) and present some of their peculiar properties, giving a historic overview. I will then give a classification of the finitely presented Abels' groups in terms of their 'ranks' and the structure of the underlying base ring. At the end of the talk we will discuss some open problems.
26.11 and 03.12.2019, 15:00, WIL A 120: Seminar Geometrie
Maxime Gheysens, Technische Universität Dresden: Topologising Automorphism Groups
When is the homeomorphism group of a topological space itself a topological group? Can the general linear group of a locally convex space be endowed with a group topology? Can we endow the automorphism group of a topological group with a compatible topology? In particular, if we start with a Polish group G, could Aut(G) be naturally seen as another Polish group? We give some answers to these questions as a particular case of a general machinery that yields topological groups from some kind of uniform spaces.
07.01.2020, 15:00, WIL A 120: Seminar Geometrie
Kevin Noack and Robert Päßler, Technische Universität Dresden: The interdisciplinary group Geometric Modeling and Visualization – Mathematical Models and Fractal Heat Exchangers
Robert will talk about his activities regarding the collection of mathematical models that everyone can visit in the Willersbau. Our research group leads a research infrastructure that uses historical material teaching models as a basis. Worldwide, those who deal with vivid models are linked. Robert reports on the digital archive of mathematical models and their derived projects.
Kevin will talk about the use of fractal structures to generate high-performing heat exchanger within the German-Austrian project instaf. He will present the workflow from the starting point, an physical optizimation problem, to the generation of CAD models, their evaluation with CFD analysis and the experimental tests of additive manufactured prototypes.
14.01.2020, 15:00, WIL A 120: Seminar Geometrie
Robert Päßler, Technische Universität Dresden: Die Sammlung mathematischer Modelle
Das Institut für Geometrie besitzt eine beeindruckende Sammlung an mathematischen Lehrmodellen. Sie bilden die Grundlage meiner Tätigkeiten in der Arbeitsgruppe "Geometrische Modellierung und Visualisierung". Ich möchte heute im ersten Teil über die Geschichte der Sammlung am Institut und zur Geschichte von mathematischen Lehrmodellen im Allgemeinen sprechen. Anschließend möchte ich über die vielfältigen Aufgaben an sowie Funktionen und Ziele von DAMM – dem Digitalen Archiv Mathematischer Modelle – informieren. Abschließend werde ich Projekte und Beispiele zum Einsatz der Sammlung in der universitären Lehre vorstellen.
27.01.2020, 15:00, WIL A 120: Seminar Geometrie
Rohan Lean, Göttingen: Bivariant K-theory as a stable ∞-category
A brief introduction of C*-algebras and ∞-categories is followed by a concrete construction of a stable ∞-category that truncates to Kasparov's bivariant K-theory. The construction is compatible with various additional structures on C*-algebras (or pro-C*-algebras), and it has a practical universal property that can be used, for example, to define a monoidal structure.
No prior knowledge of K-theory is required.